How to prove $b=c$ if $ab=ac$ (cancellation law in groups)? I want to prove for a group $G$, that if 
$$a\circ b =a\circ c$$ then this is true $$b=c$$
I started with $b=b\circ e$, but this didn't help me at all. 
Next I tried with this:
$$(a\circ b)\circ c=a\circ (b\circ c)$$ but I don't know/understand how to go further. How can I prove this equation?

Ok, we know $a,b,c \in G$
$$b = e∘b = (a^{-1}∘a)∘b = a^{-1}∘(a∘b)=a^{-1}∘(a∘c) = (a^{-1}∘a)∘c = c$$
