中文摘要：

M-P逆不具有交换性,即（AB）^＋=B^＋A^＋一般不成立,但利用投影算子的理论得到了（AB）^＋=B^＋A^＋的一些充要条件.将用矩阵秩这种新的研究方法研究广义逆的交换性使得证明变得更简洁.

英文摘要：

One of the major shortcomings of the Moor-penrose inverse is that the ＇reverse order law＇ does not always hold,that is,（AB）^＋ is not always equal to B^＋A^＋.Some scholars used the theory of projection to discuss this issue.They got a number of necessary and sufficient conditions on（AB）^＋=B^＋A^＋.In this paper,matrix rank methods are used to discuss the ＇reverse order law＇ on Moor-penrose.The proof becomes more concise.