Let A = [a_ij] be a 2 x 2 matrix such that a_ij = (, -3i+j, )/2 then a_21 is : Option 1: -1/2 Option 2: 5/2 Option 3: -5/2 Option 4: 1/2

Answer: 5/2. Solution: Substitute i=2, j=1 in a_ij = (, -3i+j, )/2. a_21 = (, -3(2)+1, )/2 = (, -5, )/2 = 5/2.

Algebra

Matrices & Determinants

Easy

common

Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} = \frac{|-3i+j|}{2}$ then $a_{21}$ is :

$-\frac{1}{2}$

$\frac{5}{2}$

$-\frac{5}{2}$

$\frac{1}{2}$

✅ Correct Option: 2

Substitute $i=2, j=1$ in $a_{ij} = \frac{|-3i+j|}{2}$ .

$a_{21} = \frac{|-3(2)+1|}{2} = \frac{|-5|}{2} = \frac{5}{2}$ .

2026: 19 May Shift 2

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:

2025: 2 June Shift 1

If $a_{ij}=i+3j$ , then the matrix of order 2 with elements as $a_{ij}$ is

2025: 30 May Shift 1

If $A = \begin{bmatrix} a & 1 & -1 \\ 0 & b & 4 \\ 4 & 4 & c \end{bmatrix}$ and $abc = 12$ , $b = 4a$ , then the value of $|A(adjA)|$ is:

2026: 18 May Shift 1

Let $A$ and $B$ be two symmetric matrices of same order, then

Match List-I with List-II

List-I	List-II
(A). $AB - BA$	(I). Neither symmetric nor Skew symmetric
(B). $BA - 2AB$	(II). Skew symmetric
(C). $AB + BA$	(III). Null matrix
(D). $(AB)^T - BA$	(IV). Symmetric

Choose the correct answer from the options given below:

2026: 19 May Shift 1

The matrix X such that it satisfies the equation: $X\begin{bmatrix} 3 & 2 \\ 1 & -1 \end{bmatrix} = \begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}$ is

2026: 15 May Shift 1

If $A = [a_{ij}]_{3\times3}, a_{ij} = 2i-j$ then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert A \vert$	I.	$4$
B.	$\vert A - I \vert$ , I is identity matrix	II.	$-7$
C.	minor of $a_{32}$	III.	$0$
D.	cofactor $a_{32}$	IV.	$-4$

Choose the correct answer from the options given below: