Is the subgroup of $GL(2,\mathbb Z)$ generated by the matrices 
$$ \left( \begin{array}{cc}
1 & 1  \\\
1 & 0 \end{array} \right) \ \ \text{and} \ \
\left( \begin{array}{cc}
2 & 1  \\\
1 & 0 \end{array} \right)
$$
free? 

I am sure this is well known, so any relevant references will be appreciated. 

My motivation comes from dynamical systems where these matrices specify two automorphisms of the 2-torus; I am interested in studying the orbits of their joint action.