CUET PG 2026 — Mathematics PYQ

To find the correct option, we need to look at the definitions of symmetric and skew-symmetric matrices.

1. Definition of a Symmetric Matrix:

A square matrix $A$ is symmetric if it is equal to its transpose:

2. Definition of a Skew-Symmetric Matrix:

A square matrix $A$ is skew-symmetric if it is equal to the negative of its transpose:

3. Combining the two conditions:

Since the problem states that $A$ is both symmetric and skew-symmetric, we can set the two expressions for $A^T$ equal to each other:

4. Solving for A:

Add $A$ to both sides of the equation:

Where $O$ represents the zero matrix (a matrix where every element is zero).

Final Answer:

The correct option is (b) A is zero matrix.