UPSC NDA Math Model Paper 9

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.