We know, that A matrix 'A' is said to be symmetric if A=AT and anti-symmetric if A=−AT Now, consider (A+AT)T=AT+(AT)T=AT+A Therefore, A+AT is always symmetric. Now, consider (A−AT)T=AT−(AT)T=AT−A =−(A−AT) Therefore, A−AT is always anti-symmetric. Hence, option (3) is correct.