The difference of two different skew-symmetric matrices is:

The correct answer is Option (4) → Skew-symmetric matrix

Let A and B be different skew-symmetric matrices of the same order, so \(A^T = -A\) and \(B^T = -B\). Using \((A - B)^T = A^T - B^T\):

    \((A - B)^T = -A + B\)
    \((A - B)^T = -(A - B)\)

So A − B is skew-symmetric. Since A and B are different, A − B is not the null matrix.