Let A be a square matrix. Then prove that `A - A^(T)` is a skew-symmetric matrix

Let A be a square matrix. Then prove that A + A ^(T) is a symmetric matrix.

Let A be a square matrix. Then prove that A A^(T) and A^(T) A are symmetric matrices.

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

Let A and B be two symmetric matrices of same order. Then show that AB-BA is a skew-symmetric matrix.

For any square matrix A,prove that A+A' is symmetric.

For any square matrix A with real number entries.Prove that A+A^' is a symmetric matrix and A-A^' is a skew symmetric matrix.

For the matrix A=[[1,5],[6,7]] , verify that A-A^T is a skew symmetric matrix

Let A be a square matrix of order 'n' then abs[KA]=

Let A be a square matrix of order 2x2 then abs[KA] is equal to

If A is square matrix, A', is its transpose, then 1/2(A-A') is a)a Symmetric matric b)a skew-symmetrix matrix c)a unit matrix d)a null matrix