Group inverse for a class 2×22×2 block matrices over skew fields

Suppose K   is a skew field. Let Kn×nKn×n denote the set of all matrices over K  . For A∈Kn×nA∈Kn×n, the matrix X∈Kn×nX∈Kn×n is said to be the group inverse of A  , if it holds that AXA=A,XAX=X,AX=XA. In this paper, we give the existence and the representation of the group inverse for block matrix M=AAB0(A,B∈Kn×n,A2=A) over skew fields, and give the existences and the representations of the group inverse for other block matrices.