If A = bmatrix 0 & l & -3 \\ -2 & 0 & 1 \\ m & -1 & 0 bmatrix is a skew symmetric matrix, then Option 1: l = 3, m = 2 Option 2: l = -3, m = 2 Option 3: l = 2, m = 3 Option 4: l = 2, m = -3

Answer: l = 2, m = 3. Solution: A skew symmetric matrix satisfies A^T = -A. This means the transpose equals the negative of the original matrix. For any skew symmetric matrix: - All diagonal elements must be 0 - Elements satisfy a_ij = -a_ji For position (1,2) and position (2,1): Position (1,2) = l Position (2,1) = -2 Using the property a_ij = -a_ji: l = -(-2) l = 2 For position (1,3) and position (3,1): Position (1,3) = -3 Position (3,1) = m Using the property a_ij = -a_ji: -3 = -m m = 3 Therefore, l = 2 and m = 3.

Algebra

Matrices & Determinants

Medium

core

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

$l = 3, m = 2$

$l = -3, m = 2$

$l = 2, m = 3$

$l = 2, m = -3$

✅ Correct Option: 3

A skew symmetric matrix satisfies $A^T = -A$ .

This means the transpose equals the negative of the original matrix.

For any skew symmetric matrix:

All diagonal elements must be 0
Elements satisfy $a_{ij} = -a_{ji}$

For position $(1,2)$ and position $(2,1)$ :

Position $(1,2) = l$

Position $(2,1) = -2$

Using the property $a_{ij} = -a_{ji}$ :

$l = -(-2)$

$l = 2$

For position $(1,3)$ and position $(3,1)$ :

Position $(1,3) = -3$

Position $(3,1) = m$

Using the property $a_{ij} = -a_{ji}$ :

$-3 = -m$

$m = 3$

Therefore, $l = 2$ and $m = 3$ .

2025: 21 May Shift 2

Match List-I with List-II

List-I (Matrix A)	List-II (Determinant of Adjoint of A)
(A) $\begin{bmatrix} 3 & 1 \\ 4 & 2 \end{bmatrix}$	(I) 9
(B) $\begin{bmatrix} 5 & -1 \\ 4 & 2 \end{bmatrix}$	(II) 8
(C) $\begin{bmatrix} 6 & -1 \\ 2 & 1 \end{bmatrix}$	(III) 14
(D) $\begin{bmatrix} 4 & 1 \\ 3 & 3 \end{bmatrix}$	(IV) 2

Choose the correct answer from the options given below:

2025: 3 June Shift 2

Assume A, B and C are matrices of order $m \times n$ , $n \times 3$ and $3 \times q$ respectively. The restrictions on $_{m,n}$ and $_q$ so that $AB + BC$ is defined are

2026: 31 May Shift 2

If matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ , then $A^2+I$ is equal to: (Where I is an identity matrix of order 2)

2025: 22 May Shift 2

If $\begin{bmatrix} ab & cd \\ a+c & b+d \end{bmatrix} = \begin{bmatrix} 2 & -3 \\ 4 & 1 \end{bmatrix}$ where $a$ , $b$ , $c$ , $d$ are integers, then which of the following are true?

(A) $a + d = 0$

(B) $b + d = 3$

(D) $c + d = 2$

Choose the correct answer from the options given below:

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:

2025: 16 May Shift 1

Let A = [aᵢⱼ]ₙₓₙ and B = [bᵢⱼ]ₙₓₙ. Then which of the following is/are true?

(A) AB = BA

(B) (AB)⁻¹ = B⁻¹ A⁻¹

(D) AB = 0 ⇒ A = 0 or B = 0

Choose the correct answer from the options given below:

If A=[0l−3−201m−10]A = \begin{bmatrix} 0 & l & -3 \\ -2 & 0 & 1 \\ m & -1 & 0 \end{bmatrix}A=​0−2m​l0−1​−310​​ is a skew symmetric matrix, then

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CUET Mathematics Past Year Questions (Topic-Wise)

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