# Thread: If x^(2)=1 then G is abelian

1. ## If x^(2)=1 then G is abelian

I'm trying to show that if x^(2)=1 for all x in G then G is an abelian group.

Attempt at the solution:

xx=1

x=x^(-1)

xy=(xy)^(-1)

xy=y^(-1)x^(-1)=yx

Does this look correct?

2. Originally Posted by Louise
I'm trying to show that if x^(2)=1 for all x in G then G is an abelian group.

Attempt at the solution:

xx=1

x=x^(-1)

xy=(xy)^(-1)

xy=y^(-1)x^(-1)=yx

Does this look correct?
yes - looks neat to me