General linear group

Description

Let $R$ be a commutative ring and let $n \ge 1$ be an integer. The general linear group $GL_n(R)$ is the set of invertible $n \times n$ matrices over $R$, with matrix multiplication as operation. It is a group: the product of invertible matrices is invertible, the identity element is $I_n$, and the inverse of $A$ is $A^{-1}$. Equivalently, $GL_n(R)$ is the group of units of the matrix ring $M_n(R)$.