= Solution
Work over the complex numbers, the usual scalar field for the finite-group <character> theory used below. A <group representation> on a nonzero vector space $V$ is a homomorphism $D:G\to GL(V)$, so $D(gh)=D(g)D(h)$ and $D(e)=I$.
A <faithful representation> is injective: distinct group elements have distinct representing maps. Equivalently, its kernel is just $\{e\}$.
An <irreducible representation> has no nonzero proper invariant subspace: if $W\subseteq V$ and $D(g)W\subseteq W$ for every $g\in G$, then $W=\{0\}$ or $W=V$. Irreducibility concerns invariant subspaces, whereas faithfulness concerns whether any group element is represented by the identity.
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