Let $G$ be a finite group. Prove following statement. $\forall g \in G$ such that $g \neq e$ $ \exists$ a complex irrep $\rho$ such that $\rho(g) \neq E$
I have no idea how to start it. I can prove this statement for cyclic group. I tried for any finite group. Assume that $ \exists g\neq e \in G$ such that $\forall $ complex irrep $\rho$ $\rho(g) = E.$ I am not sure how to continue. Can I show that $\rho(g) $ is trivial?
Thanks a lot in advance for any help! I am sorry for my bad English.