We have MN = NM M2N2(MTN)−1(MN−1)T M2N2N−1(MT)−1(N−1)T.MT = M2N.(MT)−1(N−1)TMT = −M2.N(M)−1(NT)−1MT = +2NM−1N−1MT = −M.NMM−1N−1M = −MNN−M = −M2 Note: A skew symmetric matrix of order 3 cannot be non- singular hence the question is wrong.