When I browse https://en.m.wikipedia.org/wiki/Schur%E2%80%93Weyl_duality , I saw it's proof used a fact that $U \otimes _A V$ is equal to $\mathbb{C}$ if and only if $V$ and $U$ as representation of $A$ are isomorphism, Where $A=\mathbb{C}[G]$, the group algebra of group $G$. my problem is how to get the fact.
I think it use the Schur's lemma, but I don't know how it works.