Homework Help: Absract Algebra Problem

1. Oct 8, 2009

DEMJ

1. The problem statement, all variables and given/known data

List all the elements of $$GL_n(\mathbb{Z}/2\mathbb{Z})$$. Find the order of each element, and show it is not abelian.

3. The attempt at a solution
Ok so I know that $$\mathbb{Z}/2\mathbb{Z}$$ has two elements because $$\mathbb{Z}/2\mathbb{Z} = \{ \bar{0}, \bar{1}\}$$. How does the General Linear Group effect the elements of $$\mathbb{Z}/2\mathbb{Z}$$? The Genereal Linear Group is defined as: Let F be a field. Then the general linear group $$GL_n(F)$$ is the group of invertible n x n matrices with entries in F under matrix multiplication.