Prove its abelian is this proof correct

[natasha d]

Homework Statement

(ab)^{n}= a^{n}b^{n} for any 3 consecutive numbers n \inN

Homework Equations

for an abelian group G, ab=ba \foralla,b\inG
if a\inG, a has an inverse element also \inG such that aa^{-1} = e

The Attempt at a Solution

doesnt look right but here's the attempt

http://pics.livejournal.com/jackdnutter/pic/000013d1

 

[Oster]

Your proof is a little hard to read. In your proof you seem to have proved ab=e for all a,b in G? that looks fishy...
this is a solution. https://www.physicsforums.com/showthread.php?t=529381

 

[natasha d]

that looks fishy...

yeah it does, which is why I asked. Whats wrong with it though? if someone could point out the flawed reasoning maybe it'd better my understanding of group theory.
Thanks for the link, the (ba)^{∞} proof was hilarious