The concepts of the commutative laws and generalized commutative laws of matrix multiplication on generalized inverse were defined.Using the matrix rank method and SVD,necessary and sufficient conditions about the commutative laws and generalized commutative laws of matrix multiplication on ｛1｝inverse,｛1,2｝inverse,｛1,3｝inverse and ｛1,4｝inverse were established respectively,and these conditions were compared between themselves.