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If `A` is a skew-symmetric and `n in N` such that `(A^n)^T=lambda\ A^n` , write the value of `lambda`

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Given: `A` is a skew-symmetric and `n in N` such that `(A^n)^T=lambda\ A^n`
As `(A^n)^T=(A^T)^n`
`implies (A^T)^n=lambda\ A^n`
Now as A is skew-symmetric
`implies (-A)^n=lambda\ A^n`
...
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