If A and B are matrices of same order, then (AB^T - BA^T) is always

The correct answer is Option (2) → a skew symmetric matrix

A matrix M is skew-symmetric if \(M^T = -M\). Let \(M = AB^T - BA^T\). By the reversal law \((PQ)^T = Q^T P^T\) and \((P^T)^T = P\):

    \(M^T = (AB^T)^T - (BA^T)^T\)
    \(= (B^T)^T A^T - (A^T)^T B^T\)
    \(= BA^T - AB^T\)
    \(= -M\)

So \(AB^T - BA^T\) is always a skew-symmetric matrix.