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Let M and N be two 3xx3 non - singular ...

Let M and N be two `3xx3` non - singular skew symmetric matrices such that MN = NM Let `P^(T) ` denote the transpose of P , then : `M^(2)N^(2) (M^(T)N)^(-1) (MN^(-1))^(T)` is equal to :

A

`M^(2)`

B

`-N^(2)`

C

`-M^(2)`

D

MN

Text Solution

Verified by Experts

The correct Answer is:
C
`MN + NM`
`M^(2)N^(2) (M^(T)N)^(-1) (MN^(-1))^(T) M^(2) N^(2) N^(-1) (M^(T)) ^(-1) (N^(-1))^(T) cdot M^(T)`
`= M^(2) N cdot(M^(T))^(-1) (N^(-1))^(T)M^(T)=-M^(2)cdotN(M)^(-1) (N^(T))^(-1) M^(T)`
`+ M^(2) NM^(-1) N^(-1) M^(T) = -M cdot NMM^(-1) N^(-1) M `
`=-MNM^(-1) M=-M^(2)`
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