Another group theory question

1. Nov 9, 2006

margaret23

Could you also help me start this question

show that if a^2 = e for all a in G then G must be commutative. (where e is the identity)

thanks

2. Nov 9, 2006

0rthodontist

What does aabb equal? What does abab equal?

3. Nov 9, 2006

margaret23

umm ok .. so i get that aabb must also =e .. but im not sure how to get abab

Last edited: Nov 9, 2006
4. Nov 9, 2006

JasonRox

Just show that ab = ba.

That's what you're doing. Start from there.

5. Nov 9, 2006

0rthodontist

It's (ab)(ab), so you know aabb = abab. Can you finish that?

6. Nov 12, 2006

margaret23

thanks :).. i got it now