Math Help - Coset proof

1. Coset proof

I'm having some trouble figuring out this proof:

Let H be a subgroup of G and suppose that Ha=bH for a,b in G. Show aH=Hb.

Any suggestions?

2. Re: Coset proof

Originally Posted by sfspitfire23
I'm having some trouble figuring out this proof:

Let H be a subgroup of G and suppose that Ha=bH for a,b in G. Show aH=Hb.

Any suggestions?
If e is the identity of G then $a = ea \in Ha$. Therefore $a = bh$ for some $h\in H$. So $aH = bhH = bH = Ha,$ and similarly $Hb = bH.$