For some calculation I need the precise elements of each order order. I have seen that ${\rm SL}(2,3)$ is group of order $24$ having elements: $1$ of order $1$ and $2$, $8$ elements of order $3$, $6$ elements of order $4$ and $8$ elements of order $4$.
It is known that ${\rm SL}(2,3)=\langle x,y,z:x^3=y^3=z^2=xyz \rangle$. How can we see the elements $x,y$ and $z$ in terms of matrices.
I have seen some where that $$ A= \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} $$ and $$ B= \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} $$ will generate the group ${\rm SL}(2,3)$. I wants to know how we can the presentation like above. Please help me I tried a lot but not succeeded.