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Question

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 M2N2(MTN)1(MN1)T is equal to

A
M N
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B
N2
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C
M2
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D
M2
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Solution

The correct option is B N2
Answer (Statement of the question is incorrect)
Every skew-symmetric matrix of odd order is always singular and inverse of a singular matrix does not exist. The statement of the given question seems incorrect.
If the matrix is given to be symmetric and non-singular, then
MT=M
(MN)T=MN (as MN = NM given)
M2N2(MTN)1(MN1)T
=M2N2(M N)1((NT)1MT)
=M2N2(N1M1)(N1M)
=M2NM1N1M
=M2
If there may exist a non-singular skew-symmetric matrix (which does not exist), then
M2N2(MTN)1(MN1)T=M2N2(MN)1((N1)TMT)
=M2NM1(N1(M))=M2

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