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 $M^2 N^2 (M^T N)^{-1} (MN^{-1})^T$ is equal to
Answer & explanation
Correct answer: option 3
We know
$M^T=-M$
$N^T=-N$
$MN = NM$
So $M^{-1}N^{-1}=N^{-1}M^{-1}$
$M^2 N^2 (M^TN)^{-1} (MN^{-1})^T$
$=M^2 N^2 (N^{-1} ×(M^T)^{-1})×((N^{-1})^T M^T)$
$=-M^2N^2N^{-1}M^{-1}N^{-1}M$
$=-M^2$