  Given an isolated, quasi-homogeneous singularity $X$ we prove that there is a
group isomorphism between the group of rank one reflexive sheaves on $X$ and
the free abelian group generated by $\mathbb{C}^*$-divisors, modulo linear
equivalence. When $\dim(X)=2$ we reduce the problem of finding matrix
factorizations of arbitrary reflexive $\mathcal{O}_X$-modules to the same
question on rank one reflexive sheaves. We then enumerate the matrix
factorizations of all rank one reflexive sheaves. As a consequence, we prove a
conjecture of Etingof and Ginzburg on point modules.
