P and Q Symmetric Matrices therefore Transpose of P = P ..... (1) Transpose of Q = Q ..... (2) Now Transpose of (PQ−QP)=(PQ−QP)T Using the property of Transpose,(A−B)T=(A)T−(B)T (PQ−QP)T=(PQ)T−(QP)T Using again property of transpose, (AB)T=(B)T(A)T (PQ)T−(QP)T=(Q)T(P)T−(P)T(Q)T ...........(3) Using Equations (1) and (2) in (3) we get, (PQ)T−(QP)T=QP−PQ (PQ)T−(QP)T=−(PQ−QP) So, Transpose of (PQ−QP)=(PQ−QP)T=−(PQ−QP) Which show that (PQ−QP) is a Skew Symmetric Matrix. Hence, option (4) is correct.