Further results on the group inverse of some anti-triangular block matrices (Q741391)

Suppose \(R\) is a right Ore domain with unity 1. The authors 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 two classes are given. The results extend the earlier works of \textit{X. Liu} and \textit{H. Yang} [Appl. Math. Comput. 218, No. 17, 8978--8986 (2012; Zbl 1251.15007)] and \textit{J. Zhao} and \textit{C. Bu} [Electron. J. Linear Algebra 21, 63--75 (2010; Zbl 1207.15008)]. Some results in special cases are also generalized to any ring.