Proving Commutativity in Groups with a^2 = e for all a in G

[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

 

[0rthodontist]

What does aabb equal? What does abab equal?

 

[margaret23]

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

 

[JasonRox]

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

Just show that ab = ba.

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

 

[0rthodontist]

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

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

 

[margaret23]

thanks :).. i got it now