Group inverse for two classes of 2×2 anti-triangular block matrices over right Ore domains

Suppose is a right Ore domain with identity 1. Let m×n denote the set of all m×n matrices over. In this paper, we give the necessary and sufficient conditions for the existence and explicit representations of the group inverses of the block matrices [InlineEquation not available: see fulltext.] in the following two cases, respectively: (i) A 2=A and CA=C; (ii) r(C)≤r(B) and A=DC, where Aε n×n, Bεn×m, Cεm×n, Dεn×m . The paper's results generalize some relative results of Liu and Yang (Appl. Math. Comput. 218:8978-8986, 2012). © 2012 Korean Society for Computational and Applied Mathematics.