let G be a group following that whenever a, b and c belong to G and ab = ca, then b = c. prove that G is Abelian. here is what i have for the proof: (ab)c = c(ab) let c = aba^-1 (trying to find a c which which allows for commutativity) so (ab)aba^-1 = aba^-1(ab) (ab)aba^-1 = ab(a^-1 a)b then we see that aba^-1 = b (b = c) a on both sides on the right: aba^-1 a = ba then we can see that ab = ba which proves commutativity. I am not capable of using Latex at the moment, so a^-1 means the inverse of a. How is this? Where does b = c fit into all of this? I sort of came upon it through trying to prove commutativity and figured that that is logical. So I am not really all the comfortable with it, so I am looking for maybe some insight on how to better approach a problem like this. Thanks for any help.