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.

The diagonal elements of a skew-symmetric matrix are:

The inverse of a skew symmetric matrix is

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

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

Symmetric & Skew metric matrix

The determinant of a skew symmetric matrix of odd order is

The determinant of a skew symmetric matrix of odd order is

Trace of a skew symmetric matrix is always equal to