Here is my problem:
Let $X=\begin{pmatrix} 10 & 8 \\ 8 & 1 \end{pmatrix}$ and $Y=\begin{pmatrix} 5 & 7 \\ 5 & 5\end{pmatrix}$ be two elements of $SL_2(11)$. Find a subgroup of $PSL_2(11)$ isomorphic to $A_5$.
I know that $A_5$ has a presentation as $A_5=\langle x,y|x^2=y^3=(xy)^5=1\rangle$ and $PSL_2(11)=\displaystyle\frac{SL_2(11)}{\{\lambda I|\lambda^2=1, \lambda\in GF^*(11) \}}$. How can I use $X$ and $Y$? Any help will be appreciated. Thanks