Solution
= Solution
\b[True.] If every <simple module> over $\mathbb CG$ were one-dimensional, the <Maschke theorem> and the <Artin–Wedderburn theorem> would make $\mathbb CG$ a product of copies of $\mathbb C$, hence commutative. But its <basis> elements multiply as in $G$, so commutativity of $\mathbb CG$ implies commutativity of $G$. This contradicts the assumption. Therefore a non-<Abelian> finite <group> has a <simple module> of <dimension> greater than one.