注意到:A-B=A(B逆),有
左边=(A-AB)UB = [A(AB)逆]UB= [A(A逆 U B逆) ]UB = [AA逆 U AB逆] UB
=[空 U AB逆]UB =[AB逆] UB = [AUB] [(B逆)UB] =[AUB][全空间] = AUB = 左边.
命题得证.