I'm currently reviewing my algebra for my last prelim and came across the following problem that has me stumped: If $A,B,C $ are finite Abelian groups such that $A\oplus B \cong A\oplus C$ then show that $B\cong C$. I'm not really sure where to start; the only thing that comes to mind is the fundamental theorem of finitely generated Abelian groups, I'm not sure if that's useful though.
I really only want a good hint.