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If A is a skew-symmetric matrix and n is...

If A is a skew-symmetric matrix and `n` is an odd natural numbr, write whether `A^n` is symmetric or skew-symmetric or neither of the two.

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Here, `A` is a skew-symmetric matrix.
`:. A^T = -A.`
Now, We know, `(A^n)^T = (A^T)^n`
`=>(A^n)^T = (-A)^n`
As, `n` is an odd natural number,
`:. (A^n)^T = -A^n`
It means, `A^n` will be a skew-symmetric matrix for a odd number `n`, if `A` is a skew-symmetric matrix.
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