Some results on the Drazin inverse problem

In this paper, we shall examine an additive problem of existence and presentation of (a+b)d in terms of D-invertible ring elements a and b and their Drazin inverses and we shall study the existence of the Drazin inverse of a two by two matrix with zero (2,2) entry. We partly solved a problem posed by Patrício and Hartwig (2012) 22.