Show that positive odd integral powers of a skew-symmetric matrix are skew-symmetric and positive even integral powers of a skew-symmetric matrix are symmetric.

Explanation

Here, `A` is a skew-symmetric matrix.

`:. A^T = -A.`

Now, We know, `(A^n)^T = (A^T)^n`

`=>(A^n)^T = (-A)^n->(1)`

When `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.

When `n` is an even natural number,

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