Further results on the group inverse of some anti-triangular block matrices

Suppose ℜ is a right Ore domain with unity 1. In this paper, we investigate the existence of the group inverse of some anti-triangular block matrices over ℜ and obtain the sufficient and necessary conditions for such existence. Further, the representations of the group inverse for the following two classes are given. (i) , where CA = C ; (ii) , where B ♯ exists and BA = BAB ♯ B . The results extend the earlier works of Liu et al. (in Appl. Math. Comput. 218:8978–8986, 2012 ) and Zhao et al. (in E. J. Linear Algebra 21:63–75, 2010 ). Some results in special cases are also generalized to any ring.