Question

Let $A$ be a symmetric matrix, then

• A. $(kA)^T = -kA$.
• B. $A^m$ is a symmetric matrix if $m$ is a positive integer.
• C. $A^T = -A$.
• D. $A + B$ is a symmetric matrix if $B$ is a skew symmetric matrix.

Hint:

Powers of symmetric matrices are always symmetric: $(A^m)^T = (A^T)^m = A^m$. Powers of skew-symmetric matrices are symmetric for even powers and skew-symmetric for odd powers.

Answer 1

The Correct Option is B