Let M and N be two 3 × 3 skew - symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2(MTN)−1(MN−1)T is equal to
A
M2
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B
−N2
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C
−M2
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D
MN
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Solution
The correct option is C−M2 Given, MT=−M,NT=−NandMN=NM ∴M2N2(MTN)−1(MN−1)T ⇒M2N2N−1(MT)−1(N−1)T.MT⇒M2N(NN−1)(−M)−1(NT)−1(−M)⇒M2NI(−M−1)(−N)−1(−M)⇒−M2NM−1N−1M⇒−M.(MN)M−1N−1M=−M(NM)M−1N−1M⇒−MN(MM)−1N−1M=−M(NN−1)M⇒−M2