Math Help - Group proof

1. Group proof

G is a group and $x,y\in G$.

Prove that $xy=yx$ iff $y^{-1}xy=x$ iff $x^{-1}y^{-1}xy=1$.

How can I break this statement up to prove. With iff proofs, I know we go both directions but how is it broken up when another iff is embedded in it?

2. Re: Group proof

If we have to show that we have i) iff ii) iff iii), then just prove that $i)\Rightarrow ii)$, $ii)\Rightarrow iii)$ and $iii)\Rightarrow i)$.