Let M and N be two `3xx3` nonsingular 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

Options

A. `M^(2)`
B. `-N^(2)`
C. `-M^(2)`
D. MN

Answer

C

Explanation

`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)`