Algebra

Matrices & Determinants

Easy

applied

Which of the following are true about the properties of transpose of appropriate matrices?

A. $(A+B)^T = A^T + B^T$

B. $(A-B)^T = A^T - B^T$

C. $(AB)^T = A^TB^T$

D. $(kA)^T = k(A^T)$ , where k is a scalar

Choose the correct answer from the options given below:

A, B and C only

B, C and D only

A, C and D only

A, B and D only

✅ Correct Option: 4

Transposition distributes over addition and subtraction and commutes with scalar multiplication, so A, B and D are true. For a product the order reverses, $(AB)^T=B^TA^T$ , so C is false.

2025: 15 May Shift 1

If $A = \begin{bmatrix} 0 & l & -3 \\ -2 & 0 & 1 \\ m & -1 & 0 \end{bmatrix}$ is a skew symmetric matrix, then

2026: 30 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Matrix)		LIST-II (Type of matrix)
A.	$A = [a_{ij}]_{m \times m}$ where $a_{ij} = 0\ \forall\, i \neq j$	I.	Scalar matrix
B.	$A = [a_{ij}]_{m \times 1}$	II.	Diagonal matrix
C.	$A = [a_{ij}]_{1 \times n}$	III.	Column matrix
D.	$A = [a_{ij}]_{m \times m}$ where $a_{ij} = 0\ \forall\, i \neq j$ and $a_{ij} = k\ \forall\, i = j, k \neq 0$	IV.	Row matrix

Choose the correct answer from the options given below:

2026: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) If $A = [a_{ij}]_{n \times n}$ , where $a_{ij} = \begin{cases}0, & i \ne j \\ k, & i=j, k\ne 0\end{cases}$ then A is ___	(I) Symmetric matrix
(B) If $A = [a_{ij}]_{2\times 2}$ , where $a_{ij} = \begin{cases}1, & i \ne j \\ 0, & i=j\end{cases}$ , then $A^2$ is ___	(II) Skew-Symmetric matrix
(C) If A and B are matrices of the same order, then $(AB^T - BA^T)$ is ___	(III) Identity matrix
(D) If A and B are symmetric matrices of the same order, then $(AB+BA)$ is ___	(IV) Scalar matrix

Choose the correct answer from the options given below:

2025: 13 May Shift 2

For the system $\begin{bmatrix} 2 & -3 \\ -4 & 6 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -10 \end{bmatrix}$ which of the following statements are correct?

(A) The system has no solution.

(B) The system is consistent.

(D) It has a unique solution.

Choose the correct answer from the options given below:

2026: 19 May Shift 1

If $P = \begin{bmatrix} 1 & 2 \\ -1 & 3 \end{bmatrix}$ , $Q = \begin{bmatrix} 4 & 0 \\ 1 & 5 \end{bmatrix}$ and $R = \begin{bmatrix} 2 & 0 \\ 1 & -2 \end{bmatrix}$ , then which of the following are TRUE?

(A) $(P^T)^T = P^T$

(B) $(P-Q)R = PR - QR$

(D) $(PQ)^T = Q^TP^T$

Choose the correct answer from the options given below:

2025: 27 May Shift 1

If $c_{ij}$ denotes the cofactor of element $a_{ij}$ of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \\ 0 & -3 & 2 \\ 4 & 2 & 3 \end{bmatrix}$ then the value of $c_{21} \cdot c_{33}$ is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)