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Math Help - having trouble with a proof.

  1. #1
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    having trouble with a proof.

    (a)Let (G,*) be a group such that x*x=eG for all x in G. Prove G is commutative
    (b)Give a specific example of an infinite group (G,*) such that x*x= eG for all x in G

    for a, i'm thinking that I should add in another variable? really just not sure how to begin
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  2. #2
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    Quote Originally Posted by tiasum2 View Post
    (a)Let (G,*) be a group such that x*x=eG for all x in G. Prove G is commutative
    (b)Give a specific example of an infinite group (G,*) such that x*x= eG for all x in G

    for a, i'm thinking that I should add in another variable? really just not sure how to begin
    To start on (a), take two elements x, y in G and use the fact that (x*y)*(x*y) = e_G.
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