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Let Ma n dN be two 3xx3 non singular s...

Let `Ma n dN` be two `3xx3` non singular skew-symmetric matrices such that `M N=N Mdot` If `P^T` denote the transpose of `P ,` then `M^2N^2(M^T N)^(-1)(M N^(-1))^T` is equal to `M^2` b. `-N^2` c. `-M^2` d. `M N`

A

`M^(2)`

B

`-N^(2)`

C

`-M^(2)`

D

`MN`

Text Solution

AI Generated Solution

To solve the problem, we need to evaluate the expression \( M^2 N^2 (M^T N)^{-1} (M N^{-1})^T \) given that \( M \) and \( N \) are \( 3 \times 3 \) non-singular skew-symmetric matrices and that \( MN = NM \). ### Step-by-Step Solution: 1. **Understanding Skew-Symmetric Matrices**: Since \( M \) and \( N \) are skew-symmetric, we have: \[ M^T = -M \quad \text{and} \quad N^T = -N ...
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