Question

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

Options

• AB

• AB + BA

• (A + B)²

• A − B

Answer 1

A − B

Explanation:

For skew-symmetric matrices, A′ = −A and B′ = −B. Then (A − B)′ = A′ − B′ = −A + B = −(A − B). Hence, A − B is skew-symmetric, while the other given expressions do not satisfy this property.