(1)由:A+B=AB移项得：A=AB-B即：A=(A-I)B ①两边减去(A-I)得：I=(A-I)B-(A-I) ②即：I=(A-I)(B-I)可见(A-I)可逆且(A-I)^-1=B-I(2)用(B-I)左乘①得：BA-A=(B-I)(A-I)B再用②代入就得：BA-A=B所以有：BA=A+B即：BA=AB
