2. $k$ a field and $n$ a positive integer.
$\forall x\in k,\ x.I_n\in GL(n,k)\Rightarrow (GL(n,k)\ \text{finite}\Rightarrow k\ \text{finite})$
$k\ \text{finite}\Rightarrow k^{n\times n} \text{finite}\Rightarrow GL(n,k)\ \text{finite}$