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IPMAT Matrices and Determinants Questions 2026
IPMAT Matrices and Determinants questions are an important part of the IPMAT Quant section. These questions check how well you understand the basic ideas of matrices and determinants. You may get questions on types of matrices, matrix operations, finding determinants, finding transpose, finding inverse, and solving simple questions based on these concepts.
These questions may be direct or may come as part of a longer question. The good thing is that this topic becomes much easier when your basics are clear. You do not need very advanced maths for this chapter. You only need clear concepts, regular practice, and careful solving.
In this blog, you will find a simple formula PDF, a set of practice questions with answers, and some extra questions to solve on your own. You will also learn about common mistakes students make and a few easy tips to save time in the exam.
Important Formulas for IPMAT Matrices and Determinants Questions
You only need a few basic formulas and rules to solve most Matrices and Determinants questions in IPMAT. These formulas help you solve questions on matrix operations, determinants, transpose, and inverse more easily.
You can download the full formula PDF from the link above. Here is a quick look at some of the main formulas:
Concept | Formula / Meaning |
Matrix | A matrix is a rectangular arrangement of numbers in rows and columns |
Order of a matrix | Number of rows × number of columns |
Matrix addition | Two matrices can be added only when they have the same order |
Matrix subtraction | Two matrices can be subtracted only when they have the same order |
Multiplication of a matrix by a number | Multiply each element of the matrix by that number |
Matrix multiplication | AB is possible only when number of columns of A = number of rows of B |
Determinant of a 2 × 2 matrix | If A = [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}[acbd], then ( |
Transpose of a matrix | Rows become columns and columns become rows |
Symmetric matrix | A matrix for which AT=AA^T = AAT=A |
Skew-symmetric matrix | A matrix for which AT=−AA^T = -AAT=−A |
Identity matrix | A square matrix with 1s on the main diagonal and 0s elsewhere |
Zero matrix | A matrix in which every element is 0 |
Diagonal matrix | A square matrix in which all non-diagonal elements are 0 |
Singular matrix | A square matrix with determinant 0 |
Non-singular matrix | A square matrix with a determinant not equal to 0 |
Inverse of a matrix | A matrix A−1A^{-1}A−1 such that AA−1=IAA^{-1} = IAA−1=I |
Determinant property | If determinant is 0, inverse does not exist |
Equality of matrices | Two matrices are equal when their corresponding elements are equal |
These formulas are useful for solving questions on matrix operations, determinants, inverse, transpose, and types of matrices that often come in IPMAT.
Top 5 Common Mistakes to Avoid in IPMAT Matrices and Determinants Questions
Not checking the order of matrices: Before adding, subtracting, or multiplying matrices, always check the order first.
Making mistakes in determinant calculation: Many students make errors while finding the determinant, especially in the sign or multiplication part.
Forgetting the condition for inverse: The inverse of a matrix exists only when the determinant is not 0.
Confusing transpose with inverse: Transpose and inverse are not the same. Do not mix them up.
Making small calculation mistakes: Even when the method is correct, simple calculation mistakes can lead to the wrong answer.
List of IPMAT Matrices and Determinants Questions
Here is a short set of IPMAT-style Matrices and Determinants questions to help you practise. These include common types of questions based on matrix operations, determinants, transpose, inverse, and types of matrices. Practise them regularly to become faster and more confident before your IPMAT exam.
Question 1
If a 3 X 3 matrix is filled with +1 's and - 1 's such that the sum of each row and column of the matrix is 1, then the absolute value of its determinant is
correct answer:- 4
Question 2
If inverse of the matrix $$\begin{bmatrix}2 & -0.5 \\-1 & x \end{bmatrix}$$ is $$\begin{bmatrix}1 & 1 \\2 & 4 \end{bmatrix}$$, then the value of x is
correct answer:- 1
Question 3
If $$A = \begin{bmatrix}x_1 & x_2 & 7 \\y_1 & y_2 & y_3 \\z_1 & 8 & 3 \end{bmatrix}$$ is a matrix such that the sum of all three elements along any row, column or diagonal are equal to each other, then the value of determinant of A is:
correct answer:- 288
Question 4
Suppose $$\begin{vmatrix}a & a^2 & a^3-1 \\b & b^2 & b^3-1 \\ c & c^2 & c^3-1 \end{vmatrix}=0$$, where a, b and c care distince real numbers. If a = 3, then the value of abc is ________________.
correct answer:- 1
Question 5
$$\begin{bmatrix}1&0 & 0 \\ 0 &0&1\\ 0 & 1 & 0 \end{bmatrix}$$, then the absolute value of the determinant of $$(A^9+A^6+A^3+A)$$ is ________.
correct answer:- 32
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Question 6
If A is a 3 X 3 non-zero matrix such that $$A^{2} = 0$$ then determinant of $$[(1 + A)^{2}- 50A]$$ is equal to
correct answer:- 1
Question 7
Suppose a, b and c are integers such that a > b > c > 0, and $$A =\begin{bmatrix}a & b & c \\ b & c & a \\c & a & b \end{bmatrix}$$. Then the value of the determinant of A
correct answer:- 3
Question 8
If $$A = \begin{bmatrix}1 & 2 \\3 & a \end{bmatrix}$$ where as is a real number and det $$(A^{3} − 3A^{2} − 5A) =0$$ then one of the value of a can be
correct answer:- 3
Question 9
If A, B and A + B are non-singular matrices and AB = BA, then $$2A — B — A(A + B)^{−1}A + B(A + B)^{−1}B$$ equals
correct answer:- 1
Question 10
Let P(x) be a quadratic polynomial such that $$\begin{vmatrix}P(0) & P(1)\\P(0) & P(2)\end{vmatrix} = 0$$. Let P(0) = 2 and P(1) + P(2) + P(3) = 14. Then P(4) equals
correct answer:- 3
Question 11
Let A, B, C be three 4x4 matrices such that det A = 5, det B = -3, and det $$C = \frac{1}{2}$$. Then the det $$(2AB^{-1}C^{3}B^{T})$$ is ........
correct answer:- 10
Question 12
If $$A = \begin{bmatrix}1 & 0 \\ \frac{1}{2} & 0 \end{bmatrix}$$. Then $$A^{2022}$$ is
correct answer:- 3
Question 13
If $$A = \begin{bmatrix}2 & n \\4 & 1 \end{bmatrix}$$ such that $$A^3 = 27\begin{bmatrix}4 & q \\p & r \end{bmatrix}$$, then $$p + q + r$$ equals ___________
correct answer:- 12
