Which of the following are correct? (A) If A and B are symmetric matrices such that AB = BA, then AB is symmetric. (B) If A and B are symmetric matrices of the same order, then (A+B) is a symmetric matrix. (C) If A and B are symmetric matrices of the same order, then (AB-BA) is a symmetric matix. (D) If A and B are symmetric matrices of the same order, then (AB+BA) is a skew symmetric matrix Choose the correct answer from the options given below:

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 $m = 3$.

CUET UG 2025 — Mathematics Algebra

2025mcqmedium

Which of the following are correct?

(A) If A and B are symmetric matrices such that AB = BA, then AB is symmetric.

(B) If A and B are symmetric matrices of the same order, then (A+B) is a symmetric matrix.

(D) If A and B are symmetric matrices of the same order, then (AB+BA) is a skew symmetric matrix

Choose the correct answer from the options given below:

Official previous-year question

Held on 15 May 2025 · Verified 13 Jul 2026.

Options

A
(A) and (B) only
B
(A), (B) and (C) only
C
(A), (B), (C) and (D)
D
(C) and (D) only

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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 $m = 3$ .

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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 $m = 3$ .

CUET UG 2025 — Mathematics Algebra

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CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

Your note

CUET UG Algebra in other years

More CUET UG Algebra questions

Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Algebra