Group inverse for the block matrices with an invertible subblock (Q732457)

Suppose that \(M = \left(\begin{matrix} A & B \\ C & D \end{matrix} \right)\) (\(A\) is square) is a square block matrix with an invertible subblock over a skew field \(K\). The authors presented some necessary and sufficient conditions for the existence as well as the expressions of the group inverse for \(M\) under some conditions.