Given a row block matrix [ A, B ], this paper investigates the relations between the generalized inverse [ A, B ] − and the column block matrix A − B − consisting of two generalized inverses A − and B − . The first step of the investigation is to establish a formula for the minimal rank of the difference [ A, B ] − − A − B − , the second step is to find a necessary and sufficient condition for [ A, B ] − = A − B − to hold by letting the minimal rank be zero. Seven types of generalized inverses of matrices are taken into account.