Weak monotonicity of A versus {1}-inverses nonnegative on the range space of A

This short note presents a sufficient condition under which a question raised by Peris and Subiza, namely, to find a {1}-inverse X∈Rn×m of a matrix A∈Rm×n such that A is weak monotone if and only if X is nonnegative on R(A), is answered in the affirmative.