If is skew-symmetric, then for is This question has multiple correct options

For a skew-symmetric matrix A, A^T = -A. Then (A^n)^T = (A^T)^n = (-A)^n = (-1)^n A^n. Thus if n is even, A^n is symmetric; if n is odd, A^n is skew-symmetric. Since n can be any natural number, A^n is not always symmetric (only for even n), not always skew-symmetric (only for odd n), and not necessarily diagonal. Therefore none of options A, B, C is universally true, so the correct answer is D: None of these.