If `A={:[(2,3),(4,5)],` prove that `A-A^(T)` is a skew-symmetric matrix.

If A = [(3,-5),(-4,2)] then show that A+A' is a symmetric matrix.

For the matrix A=[(1,5),(6,7)] , verify that (i) (A+A') is a symmetric matrix (ii) (A-A') is a skew symmetric matrix

If A and B are symmetric matrices, prove that AB-BA is a skew symmetric matrix.

If a square matix a of order three is defined A=[a_("ij")] where a_("ij")=s g n(i-j) , then prove that A is skew-symmetric matrix.

Express the matrix A={:[(-3,4,1),(2,3,0),(1,4,5)] as the sum of a symmetric and a skew. Symmetric matrix.

Express the marix A=|{:(3,2,3),(4,5,3),(2,4,5):}| as the sum of a symmetric matrix and a skew-symmetric matrix.

Let A and B be two square matrices of the same size such that AB^(T)+BA^(T)=O . If A is a skew-symmetric matrix then BA is

If A and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

Express the matrix A=[{:(-3,4,1),(2,3,0),(1,4,5):}] as the sum of symmetric matrix and a skew-symmetric matrix.

Express the matrix A={:[(4,2,-1),(3,5,7),(1,-2,1)]:} as the sum of a symmetric matrix and a skew-symmetric matrix.