Let M and N be two 3 × 3 non‑singular skew‑symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2 N2 (MT N)–1 (MN

Engineering

Mathematics

Inverse of a Matrix

Question

Let M and N be two 3 × 3 non‑singular skew‑symmetric matrices such that MN = NM. If P^T denotes the transpose of P, then M² N² (M^T N)^–1 (MN^–1)^T is equal to :

– M²

M²

– N²

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$∵$ MN = NM

M² N² = MN MN $∵$ (MT)^–1 = (–M)^–1 = –M^–1

Given, M²N²(M^TN)^–1. (MN^–1)^T

$= - MN \underset{I}{\underset{⎵}{MN N^{- 1} M^{- 1}}} N^{- 1} M$

= –M NN^–1 M = – M²

Although, the most suitable answer is (C), But given information is contradictory as Skew symmetric matrix of odd order cannot be non singular

* The most appropriate answer to this question is (C), but because of ambiguity in language, IIT has declared this question as bonus (marks to all students)