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Abstract
The class MMA-matrices is the subclass of the M-matrices consisting of those matrices all of whose positive integer powers are irreducible M-matrices. These matrices were recently introduced in a paper by Friedland, Hershkowitz and Schneider. In this paper, the structure of several types of generalized inverse for a singular MMA-matrix are studied. It is shown that the most natural generalized inverse is the Drazin inverse. The sign patterns and irreducibility structure of the powers of a Drazin inverse of an MMA-matrix are studied, in analogy to the well-known results for the sign patterns and irreducibility structure of the inverse of a nonsingular MMA-matrix.