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Math Help - Abelian group

  1. #1
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    Unhappy Abelian group

    Let G be a group in which a^2=e (the id.) for all elements a of G. Show that G is Abelian.
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  2. #2
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    Quote Originally Posted by r7iris View Post
    Let G be a group in which a^2=e (the id.) for all elements a of G. Show that G is Abelian.
    (ab)^2 = e
    Expand,
    abab=e
    So,
    ab=ba (since a^{-1} = a \mbox{ and }b^{-1}=b).
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