# Matrices as generators of free group.

In the introduction section of the paper Triples of $2\times 2$ matrices which generate free groups the authors mentioning some thing...

In my words:

The matrices $\begin{pmatrix}1 & 0 \\ 2 & 1\end{pmatrix}$ and $\begin{pmatrix}1 & 2 \\ 0 & 1\end{pmatrix}$ are generating the free group of two generators.

How to prove the above statement?

• Take a look at the references in the paper you are reading. – Moishe Kohan Aug 9 '13 at 22:48
• Well, one of the references is in German, the other is in Russian. So the request is perhaps not unreasonable. – Chris Godsil Aug 9 '13 at 22:54
• @ChrisGodsil: And another one (Lyndon and Ullman) is in English. – Moishe Kohan Aug 9 '13 at 22:59