CUET PYQs for Matrices and Determinants with Solutions: Practice CUET Previous Year Questions

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Matrices and Determinants is an important topic in the Mathematics section in CUET exam. Practising this topic will increase your score overall and make your conceptual grip on CUET exam stronger.

This article gives you a full set of CUET PYQs for Matrices and Determinants with explanations for effective preparation. Practice of CUET Mathematics PYQs including Matrices and Determinants questions regularly will improve accuracy, speed, and confidence in the CUET 2026 exam.

CUET PYQs for Matrices and Determinants with Solutions

1.
If $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$, $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$, $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$, then the value of the $\alpha$ is
- 7
- 4/3
- 1
- 5
View Solution
2.
If P, Q and R are three singular matrices given by $P = \begin{bmatrix} 2 & 3a \\ 4 & 3 \end{bmatrix}$, $Q = \begin{bmatrix} b & 5 \\ 2a & 6 \end{bmatrix}$ and $R = \begin{bmatrix} a^2 + b^2 - c & 1-c \\ c+1 & c \end{bmatrix}$, then the value of $(2a + 6b + 17c)$ is
- 30
- 18
- 34
- 24
View Solution
3.
Let A be a non-singular matrix of order 3 and $|A| = 15$, then $|\text{adj } A|$ is equal to
- 15
- 45
- 225
- 150
View Solution
4.
If A = $\begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then |adj A| is equal to
- 3
- 9
- 27
- 81
View Solution

5.
Match List-I with List-II
List-I (Matrix) List-II (Inverse of the Matrix)
(A) $\begin{bmatrix} 1 & 7 \\ 4 & -2 \end{bmatrix}$ (I) $\begin{bmatrix} \tfrac{2}{15} & \tfrac{1}{10} \\[6pt] -\tfrac{1}{15} & \tfrac{1}{5} \end{bmatrix}$
(B) $\begin{bmatrix} 6 & -3 \\ 2 & 4 \end{bmatrix}$ (II) $\begin{bmatrix} \tfrac{1}{5} & -\tfrac{2}{15} \\[6pt] -\tfrac{1}{10} & \tfrac{7}{30} \end{bmatrix}$
(C) $\begin{bmatrix} 5 & 2 \\ -5 & 4 \end{bmatrix}$ (III) $\begin{bmatrix} \tfrac{1}{15} & \tfrac{7}{30} \\[6pt] \tfrac{2}{15} & -\tfrac{1}{30} \end{bmatrix}$
(D) $\begin{bmatrix} 7 & 4 \\ 3 & 6 \end{bmatrix}$ (IV) $\begin{bmatrix} \tfrac{2}{15} & -\tfrac{1}{15} \\[6pt] \tfrac{1}{6} & \tfrac{1}{6} \end{bmatrix}$

List-I (Matrix)	List-II (Inverse of the Matrix)
(A) \(\begin{bmatrix} 1 & 7 \\ 4 & -2 \end{bmatrix}\)	(I) \(\begin{bmatrix} \tfrac{2}{15} & \tfrac{1}{10} \\[6pt] -\tfrac{1}{15} & \tfrac{1}{5} \end{bmatrix}\)
(B) \(\begin{bmatrix} 6 & -3 \\ 2 & 4 \end{bmatrix}\)	(II) \(\begin{bmatrix} \tfrac{1}{5} & -\tfrac{2}{15} \\[6pt] -\tfrac{1}{10} & \tfrac{7}{30} \end{bmatrix}\)
(C) \(\begin{bmatrix} 5 & 2 \\ -5 & 4 \end{bmatrix}\)	(III) \(\begin{bmatrix} \tfrac{1}{15} & \tfrac{7}{30} \\[6pt] \tfrac{2}{15} & -\tfrac{1}{30} \end{bmatrix}\)
(D) \(\begin{bmatrix} 7 & 4 \\ 3 & 6 \end{bmatrix}\)	(IV) \(\begin{bmatrix} \tfrac{2}{15} & -\tfrac{1}{15} \\[6pt] \tfrac{1}{6} & \tfrac{1}{6} \end{bmatrix}\)

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)
(A) - (I), (B) - (III), (C) - (II), (D) - (IV)
(A) - (III), (B) - (I), (C) - (IV), (D) - (II)
(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

View Solution

6.
If A and B are invertible matrices then which of the following statement is NOT correct?
- adjA = |A|A-1
- (A + B)-1= A-1 + B-1
- |A-1| = |A|-1
- (AB)-1 = B{-1}A-1
View Solution
7.
Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to
- $ 5^2 . |A| \cdot |B| $
- $ 5^3 \cdot |A| \cdot |B| $
- 5^{2} |AB|
- 5^{3} |AB|
View Solution
8.
If A = $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ and B = $\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to
- $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$
- $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$
- $\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$
- $\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$
View Solution
9.
Let AX = B be a system of three linear equations in three variables. Then the system has
(A) a unique solution if |A| = 0
(B) a unique solution if |A| $\neq$ 0
(C) no solutions if |A| = 0 and (adj A) B $\neq$ 0
(D) infinitely many solutions if |A| = 0 and (adj A)B = 0
Choose the correct answer from the options given below:
- (A), (C) and (D) only
- (B), (C) and (D) only
- (B) only
- (B) and (C) only
View Solution
10.
Let A = $\begin{bmatrix} 1 & 2 & 1 \\ 1 & 3 & 2 \\ 2 & 4 & 1 \end{bmatrix}$ and Mij, Aij respectively denote the minor, co-factor of an element aij of matrix A, then which of the following are true?
(A) M22 = -1
(B) A23 = 0
(C) A32 = 3
(D) M23 = 1
(E) M32 = -3
Choose the correct answer from the options given below:
- (A) and (B) only
- (A), (B), (C) and (E) only
- (A), (D) and (E) only
- (A), (C) and (E) only
View Solution
11.
Let A = $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ and I = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If AT + A = I, then
- $\theta = 2n\pi + \frac{\pi}{3}, n \in Z$
- $\theta = n\pi, n \in Z$
- $\theta = (2n + 1)\frac{\pi}{2}, n \in Z$
- $\theta = 2n\pi + \frac{\pi}{6}, n \in Z$
View Solution
12.
Which of the following statements is incorrect?
- If two rows or two columns of a determinant are identical, then the value of the determinant is zero.
- If all the elements in any one row of the determinant are zero, then the determinant value is zero.
- The value of the determinant remains unchanged if its rows and columns are interchanged.
- If any two rows of a determinant are interchanged, then the sign of the determinant remains unchanged.
View Solution
13.
If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to
- A
- 2A
- 3A
- 5A
View Solution
14.
If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to
- A
- 2A
- 3A
- 5A
View Solution
15.
Let A = [aij]n x n be a matrix. Then Match List-I with List-II
List-I
(A) AT = A
(B) AT = -A
(C) |A| = 0
(D) |A| $\neq$ 0
List-II
(I) A is a singular matrix
(II) A is a non-singular matrix
(III) A is a skew symmetric matrix
(IV) A is a symmetric matrix
Choose the correct answer from the options given below:
- (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
- (A) - (IV), (B) - (III), (C) - (I), (D) - (II)
- (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
- (A) - (I), (B) - (II), (C) - (IV), (D) - (III)
View Solution

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CUET PYQs for Matrices and Determinants with Solutions: Practice CUET Previous Year Questions

CUET PYQs for Matrices and Determinants with Solutions

1.
If \(A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}\), \(X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}\), \(B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}\) and \(AX = B\), then the value of the \(\alpha\) is

2.
If P, Q and R are three singular matrices given by \(P = \begin{bmatrix} 2 & 3a \\ 4 & 3 \end{bmatrix}\), \(Q = \begin{bmatrix} b & 5 \\ 2a & 6 \end{bmatrix}\) and \(R = \begin{bmatrix} a^2 + b^2 - c & 1-c \\ c+1 & c \end{bmatrix}\), then the value of \((2a + 6b + 17c)\) is

3.
Let A be a non-singular matrix of order 3 and \(|A| = 15\), then \(|\text{adj } A|\) is equal to

4.
If A = $\begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then |adj A| is equal to

6.
If A and B are invertible matrices then which of the following statement is NOT correct?

7.
Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to

8.
If A = $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ and B = $\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to

11.
Let A = $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ and I = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If AT + A = I, then

12.
Which of the following statements is incorrect?

13.
If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to

14.
If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to

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CUET PYQs for Matrices and Determinants with Solutions

1.If \(A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}\), \(X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}\), \(B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}\) and \(AX = B\), then the value of the \(\alpha\) is

2.If P, Q and R are three singular matrices given by \(P = \begin{bmatrix} 2 & 3a \\ 4 & 3 \end{bmatrix}\), \(Q = \begin{bmatrix} b & 5 \\ 2a & 6 \end{bmatrix}\) and \(R = \begin{bmatrix} a^2 + b^2 - c & 1-c \\ c+1 & c \end{bmatrix}\), then the value of \((2a + 6b + 17c)\) is

3.Let A be a non-singular matrix of order 3 and \(|A| = 15\), then \(|\text{adj } A|\) is equal to

4.If A = $\begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then |adj A| is equal to

6.If A and B are invertible matrices then which of the following statement is NOT correct?

7.Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to

8.If A = $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ and B = $\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to

11.Let A = $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ and I = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If AT + A = I, then

12.Which of the following statements is incorrect?

13.If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to

14.If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to

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1.
If \(A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}\), \(X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}\), \(B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}\) and \(AX = B\), then the value of the \(\alpha\) is

2.
If P, Q and R are three singular matrices given by \(P = \begin{bmatrix} 2 & 3a \\ 4 & 3 \end{bmatrix}\), \(Q = \begin{bmatrix} b & 5 \\ 2a & 6 \end{bmatrix}\) and \(R = \begin{bmatrix} a^2 + b^2 - c & 1-c \\ c+1 & c \end{bmatrix}\), then the value of \((2a + 6b + 17c)\) is

3.
Let A be a non-singular matrix of order 3 and \(|A| = 15\), then \(|\text{adj } A|\) is equal to

4.
If A = $\begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then |adj A| is equal to

6.
If A and B are invertible matrices then which of the following statement is NOT correct?

7.
Let A = [aij]2x3 and B = [bij]3x2, then |5AB| is equal to

8.
If A = $\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ and B = $\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to

11.
Let A = $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ and I = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If AT + A = I, then

12.
Which of the following statements is incorrect?

13.
If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to

14.
If A is a square matrix and I is the identity matrix of same order such that A2 = I, then (A - I)3 + (A + I)3 - 3A is equal to