Let $A$ be a nonsingular M-Matrix. Then $A$ has only eigenvalues with positive real parts.

Question

Let $A$ be a nonsingular M-Matrix. How to show that the eigenvalues of $A$ have only positive real parts ?

Here a nonsingular M-Matrix $Q = (q_{ij})$ is a nonsingular Matrix such that $q_{ij} \leq 0 \: \forall i \neq j$ and $q_{ii} > 0$

My ideas:
I managed to show that the inverse $A^{-1} \geq 0$ entrywise. But I don't know how I could continue from there.