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

The diagonal elements of a skew-symmetric matrix are:

Prove that diagonal elements of a skew symmetric matrix are all zeroes.

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

Which one of the following is wrong? (A) The elements on the main diagonal of a symmetric matrix are all zero (B) The elements on the main diagonal of a skew - symmetric matrix are all zero (C) For any square matrix A,AA' is symmetric (D) For any square matrix A,(A+A')^(2)=A^(2)+(A')+2AA'

Which one of the following is wrong? 1.The elements on the main diagonal of a symmetric matrix are all zero 2. The elements on the main diagonal of a skew-symmetric matrix are all zero 3. For any square matrix A,(1)/(2)(A+A') is symmetric 4. For any square matrix A,(1)/(2)(A-A') is skew-symmetric

If A is skew symmetric matrix of order 3 then det A is (A)0 (B)-A (C)A (D)none of these

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.

A matrix which is symmetric as well as skew symmetric (A)null matrix (B)diagonal matrix (C)both A and B (D)none of these

If every non diagonal element of a square matrix is zero and every diagonal element is equal then the matrix is called