Show that `(A+A')` is symmetric matrix, if A = `((2,4),(3,5))`.

Show that A is a symmetric matrix if A= [ (1,0), (0, -1)]

Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric if A^2=(A^T)^2

Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric iff A^2=(A^T)^2 .

If A=[[2,4],[5,6]] , show that (A-A^T) is a skew symmetric matrix, where A^T is the transpose of matrix A.

If A=[[3,4],[5,1]] , show that A-A^T is a skew symmetric matrix, where A^T denotes the transpose of matrix A

If A=[[4,1],[5,8]] , show that A+A^T is symmetric matrix, where A^T denotes the transpose of matrix A

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.

A A' is always a symmetric matrix for any matrix A.

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to