Group Actions · Hard problem

$GL(2,\mathbb Z_3)$, the invertible $2\times2$ matrices with entries mod $3$, acts on the $8$ nonzero vectors of $\mathbb Z_3^2$ by $M\cdot v=Mv\bmod3$. Given $|GL(2,\mathbb Z_3)|=48$ and that this action is transitive, find $|\operatorname{Stab}((1,0))|$.