In Gallian Ch 5 Permutation Groups, Ex 12 is as follows:

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If a permutation $\displaystyle \alpha$ is even prove that $\displaystyle {\alpha}^{-1}$ is even.

Further, if a permutation $\displaystyle \alpha$ is odd prove that $\displaystyle {\alpha}^{-1}$ is odd.

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Can anyone help with this problem. Be grateful for some help

Peter