Let G be a group with the following property: Whenever a,b and c belong to G and ab = ca, then b=c. Prove that G is abelian.
The Attempt at a Solution
I started with the hypothesis ab=ca and solved for b and c using inverses. I found b=(a-1)ca and c=ab(a-1). Because the hypothesis says b=c I set them equal. (a-1)ca=ab(a-1). But I'm having trouble getting anywhere useful after that. Hints or suggestions if I'm on the right track???