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Prove that a^m is conjugate to only a^-m, and that a^m8b is conjugate to a^(m+2k)*b, for any integer k.

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Let the dihedral group D_n be given by elements "a" of order "n" and "b" of order 2, subject to the identity b*a=a^-1*b. Prove that a^m is conjugate to only a^-m, and that a^m8b is conjugate to a^(m+2k)*b, for any integer k.

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This solution is comprised of a detailed explanation to prove that a^m is conjugate to only a^-m, and that a^m8b is conjugate to a^(m+2k)*b, for any integer k.

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Proof:
We know , where and .
To find conjugate of , we ...

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