If `B` is a skew-symmetric matrix, write whether the matrix `A B\ A^T` is symmetric or skew-symmetric.

If B is a skew-symmetric matrix, write whether the matrix A BA^T is symmetric or skew-symmetric.

If B is a symmetric matrix, write whether the matrix A B\ A^T is symmetric or skew-symmetric.

If A is a symmetric matrix, write whether A^T is symmetric or skew-symmetric.

If A is a symmetric matrix, write whether A^T is symmetric or skew-symmetric.

For any square matrix write whether A A^T is symmetric or skew-symmetric.

It A is a symmetric matrix, write whether A^T is symmetric or skew - symmetric matrix.

If A is a non-singular symmetric matrix, write whether A^(-1) is symmetric or skew-symmetric.

If A and B are symmetric matrices of the same order, write whether A B-B A is symmetric or skew-symmetric or neither of the two.

If A is a skew-symmetric matrix and n is an odd natural number, write whether A^n is symmetric or skew-symmetric or neither of the two.

Let Aa n dB be two nonsinular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following are correct? (a) . B^T A B is symmetric matrix (b) . if A is symmetric B^T A B is symmetric matrix (c) . if B is symmetric B^T A B is skew-symmetric matrix for every matrix A (d) . B^T A B is skew-symmetric matrix if A is skew-symmetric