Let A and B be two group invertible matrices, we study the rank, the nonsingularity and the group invertibility of A − B, AA − BB , c 1 A + c 2 B, c 1 A + c 2 B + c 3 AA B where c 1 , c 2 are nonzero complex numbers. Under some special conditions, the necessary and sufficient conditions of c 1 A + c 2 B + c 3 AB and c 1 A + c 2 B + c 3 AB + c 4 BA to be nonsingular and group invertible are presented, which generalized some