Given expression : M2 N2 (MTN) -1 (MN-1)T
= M2N2 (-MN)-1 (MN-1)T [ Since M is a skew symmetric matrix , so MT = -M]
= - M2N2 . N-1M-1 .(NT)-1 MT
[Since for any two matrices A and B , (AB)-1 = B-1A-1 and
(AB)T = BT AT and
(A-1)T = (AT)-1 ]
= - M2 N2 N-1 M-1 (-N)-1(-M)
= - M. M N M-1 (-N)-1(-M) [ Since for any matrix A , A A-1 = I where I is identity matrix]
= - M N M M-1 (-N)-1(-M) [Since given in the question MN = NM]
= - M2 [Since middle M,M-1 and N,N-1 are eliminated using A A-1 = I]
Hence C) option should be the correct option.