If A is a matrix of order n such that `A^(T)A=I` and X is any matric such that `X=(A+I)^(-1) (A-I)`, then show that X is skew symmetric matrix.

If A=[3-41-1], show that A-A^(T) is a skew symmetric matrix.

If A and B are two symmetric matrix of same order,then show that (AB-BA) is skew symmetric matrix.

If AB are symmetric matrices of same order then show that AB-BA is a skew symmetric matrix.

For any matrix a show that A+A^(T) is symmetric matrix

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

If A is a skew-symmetric matrix of order 3 ,then the matrix A^(4) is

If A is a skew-symmetric matrix of order 3, then |A|=

Let A and B be symmetric matrices of the same order. Then show that : A+B is a symmetric matrix

If A be a real skew-symmetric matrix of order n such that A^(2)+I=0 , I being the identity matrix of the same order as that of A, then what is the order of A?