Let $G$ be a finite group.
(1) Let $K$ be a field. Show that $G$ has a finite-dimensional fait hful $K$-linear representation.
(2) Show that $G$ has a faithful one-dimensional complex repr esentation if and only if $G$ is cyclic.
(3) Assume moreover that $G$ is commutative. Let $n \geq 1$ be an integer. Show that $G$ has a faithful $n$-dimensional complex re presentation if and only if $G$ can be generated by $n$ elements.
(4) Classify all finite groups having a faithful 2-dimensional re al representation.