Each diagonal element of a skew symmetric matrix is (A) zero (B) negative (C) positive (D) non real

The inverse of a diagonal matrix is a. a diagonal matrix b. a skew symmetric matrix c. a symmetric matrix d. none of these

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

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.

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.

Rank of a non zero matrix is always (A) 0 (B) 1 (C) gt1 (D) gt0

A square matix A is a called singular if det A is (A) negative (B) zero (C) positive (D) non-zero

If A is a square matrix, then A A is a (a) skew-symmetric matrix (b) symmetric matrix (c) diagonal matrix (d) none of these

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

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