# Abstract Algebra Problem (should be easy)?

1. Sep 29, 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

I am confused right from the get go about $$GL_n(\mathbb{Z}/2\mathbb{Z})$$.

I think the $$L_n(\mathbb{Z}/2\mathbb{Z})$$ part means there are a n x n matrices whose elements are $$\mathbb{Z}/2\mathbb{Z}$$. Is that correct to say? Also what does the group $$G$$ have to do in the problem? Any help is appreciated because I am struggling atm to even get started on this problem.

2. Sep 29, 2009

### aPhilosopher

I don't know much about finite fields but GLn(F) is the "General Linear" Group and is the set of invertible (i.e. non-singular) matrices with components in F.