We have a the presentation ${\rm SL}(2,3)=\langle x,y,z:x^3=y^3=z^2=xyz \rangle$. Can we do the same for SL$(n,\mathbb{Z}_p).$ I have seen the presentation of SL$(n,\mathbb{Z})$ the presentation of $SL(2,\mathbb{Z})$.
How can we give a presentation of SL$(2,\mathbb{Z}_p)?$