Representations for the Drazin inverses of 2 × 2 block matrices

Let M denote a 2 × 2 block complex matrix ABCD, where A and D are square matrices, not necessarily with the same orders. In this paper explicit representations for the Drazin inverse of M are presented under the condition that BDiC = 0 for i = 0, 1, … , n − 1, where n is the order of D.