General Linear Group

Def

The general linear group is the group of all matrices in $A\in M_{n,n}(F)$ such that $A$ is invertible. It is denoted as below : $G{L}_n(F)=\{\text{all }A\in M_{n,n}\mid \exists A^{-1}\in M_{n,n}(F)\}$ Group under matrix multiplication

• e is the identity matrix
• $A\mapsto A^{-1}$

It is non-commutative!

• $AB\ne BA$