Let M and N be two 2n × 2n 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
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(In JEE this question was bonus because in JEE instead of 2n × 2n, 3 × 3 was given and we know that there is no non-singular 3×3 skew symmetric matrix).
Sol. Data inconsistent
A 3 × 3 non-singular matrix cannot be skew-symmetric
However considering M, N matrices as even order, we obtain correct answer.
M 2 N 2 (M T N) –1 (MN –1 ) T = M 2 N 2 N –1 (M T ) –1 (N –1 ) T M T ⇒ – M 2 N 2 N –1 M –1 N –1 M
⇒ – M 2 NM –1 N –1 M ⇒ – MNN –1 M ⇒ –M 2
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