Which of the following is correct?

Let A be a symmetric matrix.Then, (An)′ = (AAA … n times)′= (A′ A′ A′ … A′ n times)= (A′ )n = An                      (∵ A′ = A)∴ An is also a symmetric matrix.Now, let A be a skew-symmetric matrix. Then A′ = –A.We have, (An)′ = (AAA … n times)= (A′ A′ A′ … A′ n times)                [∵ (AB)′ = B′ A′]= (A′ )n = (– A)n                             (∵ A′ = –A)= (–1)n An=An   if n is even-An  if n is odd  Hence, An is symmetric if n is even and skew-symmetric if n is odd.The correct option is (A), (B), (C) and (D)