JEE Advanced 2013 Paper 1

(A) ‌‌(NTMN)T = NTMT N is symmetric if M is symmetric and skew-symmetric if M is skew-symmetric
(B) (MN−NM)T =(MN)T−(NM)T =NM−MN =−(MN−NM) skew symmetric
(C) (MN)T =NTMT=NM ≠MN hence NOT correct
(D)standard result is adj(MN) = (adjN) (adj M)] ≠ (adjM) (adjN)