Nonnegativity of principal minors of generalized inverses of P0-matrices

We derive a necessary and sufficient condition under which a reflexive generalized inverse of a singular P₀-matrix is again a P₀-matrix. Simpler conditions are obtained when the rank of the matrix is n?1, where n is the order of the matrix. We then consider the application of these results to singular M-matrices of order n and rank n?1. In particular, for this case we prove that the Moore-Penrose inverse is a P₀-matrix.