Question

If A and B are symmetric matrices of same order, then which of the following matrices is a skew-symmetric matrix?

Options

• A² + В²

• A² − В²

• AB + BA

• AB − BA

Answer 1

AB − BA

Explanation:

Given that A and B are symmetric, so A^T = A,  B^T = B.

(AB − BA)^T = B^TA^T − A^TB^T

= BA − AB

= −(AB − BA)

Hence, AB − BA is skew-symmetric.