# Definitions The general linear group of order $n$ is the set of $n\times n$ denoted as $GL_{2}(\mathbb{R}) = \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} : a, b,c,d \in \mathbb{R} \text{ and } ad-bc \neq 0 \right\} $ - [[The General Linear Group of Order 2 is a Group Under Matrix Multiplication]].