The matrix type of purely infinite simple Leavitt path algebras

Let R denote the purely infinite simple unital Leavitt path algebra L(E). We completely determine the pairs of positive integers (c, d) for which there is an isomorphism of matrix rings M _c (R) ≌ M _d (R), in terms of the order of [1 _R ] in the Grothendieck group K ₀(R).