Let $R$ be a local ring with residue field $k$. Let $A$ be an $R$-algebra which is finitely generated as $R$-module. I want to show that the maximal ideals of $A$ are in one-to-one correspondence with the maximal ideals of $A \otimes_R k$.
I have a gut feeling that one should use the Nakayama Lemma, but I fail to find the right way in which to apply it. I would be thankful if someone could help me out here.