Show that `A` is skew symmetric matrix if `A =[[ 0,5], [-5,0]]`

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

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

Construct an orthogonal matrix using the skew- symmetric matrix A=[[0,2],[-2,0]].

If A=[[3,-4], [1,-1]] , show that A-A^T is a skew symmetric matrix.

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 is skew-symmetric matrix, then trace of A is

If A is a skew-symmetric matrix of odd order n , then |A|=0

Prove that inverse of a skew-symmetric matrix (if it exists) is skew-symmetric.

Trace of a skew symmetric matrix is always equal to