The inverse of skew - symmetric matrix of odd order

The inverse of a skew-symmetric matrix of odd order a. is a symmetric matrix b. is a skew-symmetric c. is a diagonal matrix d. does not exist

Consider the matrix A=[{:(0,-h,-g),(h,0,-f),(g,f, 0):}] STATEMENT-1 : Det A = 0 STATEMENT-2 :The value of the determinant of a skew symmetric matrix of odd order is always zero.

If A is a skew-symmetric matrix of odd order n , then |A|=0

If A is a skew-symmetric matrix of odd order n , then |A|=O .

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

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

If matric A is skew-symmetric matric of odd order, then show that tr. A = det. A.

Let A be a skew-symmetric matrix of even order, then absA

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.

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.