Expert Maths Tutoring in the UK - Boost Your Scores with Cuemath (2023)

We determine whether a matrix is a singular matrix or a non-singular matrix depending on its determinant. The determinant of a matrix 'A' is denoted by 'det A' or '|A|'. If the determinant of a matrix is 0, then it is said to be a singular matrix. Why do we need to have a specific name for the matrices with determinant 0? Let us see.

Let us learn more about the singular matrix along with its definition, formula, properties, and examples.

1.What is a Singular Matrix?
2.Identifying a Singular Matrix
3.Properties of Singular Matrix
4Singular Matrix and Non-Singular Matrix
5.Theorem to Generate Singular Matrices
6.FAQs on Singular Matrix

What is a Singular Matrix?

A singular matrix is a square matrix if its determinant is 0. i.e., a square matrix A is singular if and only if det A = 0. We know that the inverse of a matrix A is found using the formula A-1 = (adj A) / (det A). Here det A (the determinant of A) is in the denominator. We are aware that a fraction is NOT defined if its denominator is 0. Hence A-1 is NOT defined when det A = 0. i.e., the inverse of a singular matrix is NOT defined. i.e., there does not exist any matrix B such that AB = BA = I (where I is the identity matrix).

From the above explanation, a square matrix 'A' is said to be singular if

  • det A = 0 (which is also written as |A| = 0) (or)
  • A-1 is NOT defined (i.e., A is non-invertible).

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Identifying a Singular Matrix

To determine/identify whether a given matrix is singular we need to check for two conditions:

  • check whether A is a square matrix.
  • check whether det A = 0.

Here are few examples to find whether a given matrix is singular.

  • A = \(\left[\begin{array}{rr}3 & 6 \\ \\ 2 & 4 \end{array}\right]\) is a singular matrix because
    it is a square matrix (of order 2 × 2) and
    det A (or) |A| = 3 × 4 - 6 × 2 = 12 - 12 = 0.
  • A = \(\left[\begin{array}{rr}1 & 2 & 2 \\ 1 & 2 & 2\\ 3 & 2&-1 \end{array}\right]\) is a singular matrix because
    it is a square matrix (of order 3 × 3) and
    as det A (or) |A| = 0 (as the first two rows are equal).

Properties of Singular Matrix

Here are some singular matrix properties based upon its definition.

  • Every singular matrix is a square matrix.
  • The determinant of a singular matrix is 0.
  • The inverse of a singular matrix is NOT defined and hence it is non-invertible.
  • By properties of determinants, in a matrix,
    * if any two rows or any two columns are identical, then its determinant is 0 and hence it is a singular matrix.
    * if all the elements of a row or column are zeros, then its determinant is 0 and hence it is a singular matrix.
    * if one of the rows (columns) is a scalar multiple of the other row (column) then the determinant is 0 and hence it is a singular matrix.
  • A null matrix of any order is a singular matrix.
  • The rank of a singular matrix is definitely less than the order of the matrix. For example, the rank of a 3x3 matrix is less than 3.
  • All rows and columns of a singular matrix are NOT linearly independent.

Singular Matrix and Non-Singular Matrix

A non-singular matrix, as its name suggests, is a matrix that is NOT singular. Thus, the determinant of a non-singular matrix is a nonzero number. i.e., a square matrix 'A' is said to be a non singular matrix if and only if det A ≠ 0. Then it is obvious that A-1 is defined. i.e., a non-singular matrix always has a multiplicative inverse. Thus, we can summarize the differences between the singular matrix and non-singular matrix as follows:

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Singular MatrixNon Singular Matrix
A matrix 'A' is singular if det (A) = 0.A matrix 'A' is nonsingular if det (A) ≠ 0.
If 'A' is singular then A-1 is NOT defined.If 'A' is nonsingular then A-1 is defined.
Rank of A < Order of A.Rank of A = Order of A.
Some rows and columns are linearly dependent.All rows and columns are linearly independent.
If 'A' is singular then the system of simultaneous equations AX = B has either no solution or has infinitely many solutions.If 'A' is non singular then the system of simultaneous equations AX = B has a unique solution.
Example: \(\left[\begin{array}{rr}3 & 6 \\ \\ 1 & 2 \end{array}\right]\) is singular as
\(\left|\begin{array}{rr}3 & 6 \\ \\ 1 & 2 \end{array}\right|\) = 3 × 2 - 1 × 6 = 6 - 6 = 0.
Example: \(\left[\begin{array}{rr}3 & 2 \\ \\ 1 & -2 \end{array}\right]\) is non-singular as
\(\left|\begin{array}{rr}3 & 2\\ \\ 1 & -2 \end{array}\right|\) = 3 × -2 - 1 × 2 = -6 - 2 = -8 ≠ 0.

Theorem to Generate Singular Matrices

There is one important theorem on singular matrix that can actually be used to generate a singular matrix and the theorem says: "The product of two matrices A = [A]n × k and B = [B]k × n (where n > k) is a matrix AB of order n × n and is always singular". By this theorem:

  • The product AB of two matrices A of order n × 1 and B of order 1 × n is singular always.
  • The product AB of two matrices A of order n × 2 and B of order 2 × n is also singular, etc.

Using this theorem, one can generate a singular matrix by multiplying two randomly generated matrices of orders n × k and k × n where n > k.

Related Topics:

  • Diagonal Matrix
  • Orthogonal Matrix
  • Inverse of 3x3 Matrix
  • Symmetric Matrix

FAQs on Singular Matrix

What Does a Singular Matrix Mean?

A singular matrix means a square matrix whose determinant is 0 (or) it is a matrix that does NOT have a multiplicative inverse.

How do You Know if a Matrix is Singular Matrix?

We can say that a matrix 'A' is singular if one of the following conditions is satisfied.

  • If determinant of A = 0 (or)
  • If A is non-invertible.

What is Singular Matrix Formula?

We know that a singular matrix determinant is 0. Thus, the formula for the singular matrix is "A is singular if and only if det(A) = 0".

Why is It Called a Singular Matrix?

The word "singular" means "exceptional" (or) "remarkable". A singular matrix is specifically used to determine whether a matrix has an inverse, rank of a matrix, uniqueness of the solution of a system of equations, etc. It is also used for various purposes in linear algebra and hence the name.

What is a Singular Matrix 3x3?

The determinant of a singular matrix is 0. An example of a 3x3 singular matrix is \(\left[\begin{array}{rr}2 & 1 & -1 \\ 1 & 0 & 1\\ 2 & 1&-1 \end{array}\right]\) is singular as its determinant is zero (as its first and third rows are equal).

What Makes a Matrix A a Singular Matrix?

If the determinant of A is 0 then A is singular. If there is no matrix B such that AB = BA = I, then it means that A has no inverse and in this case also, A is said to be singular.

What is the Rank of a Singular Matrix?

If A is a singular matrix of order n, then it means that det A = 0. Then the rank of the matrix is definitely less than the order of the matrix. i.e., rank(A) < n.

What are Singular and Non Singular Matrices?

A singular matrix is a matrix whose determinant is 0 and hence it has no inverse. On the other hand, a non-singular matrix is a matrix whose determinant is NOT 0 and hence it has an inverse.

What is Singular Matrix Determinant?

A singular matrix has no inverse. We know that the inverse of a matrix A is (adj A)/(det A) and it does NOT exist when det A = 0. Therefore, the determinant of a singular matrix is 0.


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Cuemath is an Indian-based tutoring firm which teaches K-12 math to school-age children all over the world, including the United States.

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The national average cost of maths tutoring in the UK is £28 per hour, and quite often you'll spend well over £30 an hour. Of course, private maths tutor fees vary based on your location. If you want a private tutor to come to your home in London, you're probably going to pay more than £30 per hour.

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Cuemath has been used by more than 200,000 students across 20+ countries, giving students not only extra help, but foundational math skills.

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The greater than symbol is >. For example, 8 > 7 is read as '8 is greater than 7'. The less-than sign is '<'.

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Cuemath Cuemath Teacher salary in India ranges between ₹ 1.0 Lakhs to ₹ 5.5 Lakhs with an average annual salary of ₹ 2.8 Lakhs.

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Cuemath vs Vedic Maths for Kids

Whereas Cuemath is a pictorial method of teaching math to kids. Abacus can be a part of Cuemath which is used as a tool to teach math concepts to kids. #2 Vedic maths enhances inner abilities like Memory, speed, accuracy, concentration, and learning abilities.

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Cuemath is backed by Capital G and is present in over 20+ countries.

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Cuemath is built by Cuelearn Pvt Ltd, a math education company founded by Manan Khurma in 2014.

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How much does a private maths tutor earn UK? ›

The average maths tutor salary in the United Kingdom is £29,999 per year or £15.38 per hour. Entry level positions start at £25,940 per year while most experienced workers make up to £50,830 per year.

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Range of Prices for A level Tutors in the UK

On the lower end, A-level tutors may charge around £15-£20 per hour. At the middle range, the hourly rate can be between £20-£30 per hour. On the higher end, some A-level tutors may charge £50 per hour or more.

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Founded in 2013 by Manan Khurma, Cuemath is an ed tech company focused on math learning for K-12 students. Our mission is to make the world's children great at math, and create invincible problem-solvers who will go on to solve humanity's greatest problems.

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Cuemath's operating revenue grew 63.1% to Rs 148.05 crore in FY22 from Rs 90.77 crore in FY21, according to the company's annual financial report with the Registrar of Companies (RoC). Cuemath provides Math classes for the K-12 segment and helps students prepare for school and competitive tests.

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The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is one of the most prestigious mathematical competitions in the world. The first IMO was held in Romania in 1959.

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Top 5 Math Classes to Prepare for the Future
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There is no "highest level of math". In college they will offer graduate level classes which can cover topics deeper than is typically discussed in the undergraduate curriculum such as algebraic topology, differential geometry, algebraic geometry, category theory etc.

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When negotiating a salary for a new job. If you are negotiating the salary for a new position or a job at a new company, asking for 10% to 20% more than what you currently make is often the general rule.

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How long does it take to learn Vedic Maths? It depends on the person who takes it, generally takes from 30 hrs to 60 hrs to complete the course.

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Abacus in short is a skill development program like Vedic Mathematics or Art. On the other side, CueMath which started in India deals with concepts of class math like Number Theory, Time and Money, Geometry, Algebra etc., which are taught in Schools.

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Cuemath announces layoffs, founder Manan Khurma reassumes CEO role.

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Manan Khurma, founder and chairman of Cuemath took to LinkedIn, where he also said that current CEO Vivek Sunder will be transitioning to an advisory role.

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Jun 23, 2023

What qualifications do you need to be a maths tutor UK? ›

To become a tutor, you should get your A Levels in the subject you want to teach from either a sixth form or a college. After that you have a few options: a maths degree is the obvious choice. However, there are other related undergraduate degrees that also will provide you with the skills needed to teach maths.

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The average hourly rate of private tuition for levels of study in the UK: Primary (age 7–11): £22 per hour. Secondary (age 11–14): £21 per hour. GCSE level (age 14–16): £22 per hour.

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U.S. ranks near the bottom

On a scale of 0–1,000, the average score in math proficiency among education systems ranged from 592 in China to 326 in the Dominican Republic.

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U.S. adults have basic numeracy skills. In the United States, adults weighed in at an average numeracy rate of 253 out of 500. That puts us at level 2, or basic, numeracy skills.

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Contributor. The United States of America has dropped from second place in 2020 to third place in 2021 in a ranking of the performance of secondary school students on international science and math competitions.

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The Cuemath way has found resonance all over the world - our students come from over 70 countries and we are backed by marquee investors such as Alpha Wave, Sequoia, Lightrock, Manta Ray and Capital G.

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Kumon opened their first United States locations in 1983, and by 1985, Kumon reached 1.4 million students. Kumon soon added more educational subjects, leading them to change their name from Kumon Institute of Mathematics to Kumon Institute of Education.

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Both are technically right! While “math” is more common, “maths” is totally acceptable to use, as well, for the short version of the word mathematics.

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Here are the 10 countries with the most top-ranked math scientists:
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Why is Kumon so successful? ›

Kumon builds skills through daily practice

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Kumon places great importance on self-learning, encouraging students to read the worksheets, think, and do the exercises on their own. The ability to study independently helps students become proactive and assists them in the pursuit of their goals and aspirations.


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