Show that positive odd integral powers of a skew-symmetric matrix are skew-symmetric and positive even integral powers of a skew-symmetric matrix are symmetric.

STATEMENT -1 All positive odd integral powers of a skew - symmetric matrix are symmetric. STATEMENT-2 : All positive even integral powers of a skew - symmetric matrix are symmetric. STATEMENT-3 If A is a skew - symmetric matrix of even order then |A| is perfect square

Show that all positive integral powers of a symmetric matrix are symmetric.

Show that all positive integral powers of a symmetric matrix are symmetric.

The inverse of skew - symmetric matrix of odd order

Prove that inverse of a skew-symmetric matrix (if it exists) is skew-symmetric.

If A is a skew-symmetric matrix and n is a positive even integer, then A^(n) is

If A is skew-symmetric matrix then A^(2) is a symmetric matrix.

Trace of a skew symmetric matrix is always equal to

If A is a skew-symmetric matrix and n is odd positive integer, then A^n is

Show that the elements on the main diagonal of a skew-symmetric matrix are all zero.