# Math Help - having trouble with a proof.

1. ## 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

2. Originally Posted by tiasum2
(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 $(x*y)*(x*y) = e_G$.