# An elementary proof in matrix algebra

If $A$ and $B$ are two conformable matrices,and $AB = A$ and $BA = B$ then prove that A and B are idempotent matrices.

This may be trivial but I am not sure how to proceed on this.

-

$$Ax = ABx = A(BA)x = (AB)Ax = AAx$$
Tell me if I do something like this :$A = AB = A(BA) = (AB)A = AA = A^2$, any problem? :) –  Quixotic Dec 26 '10 at 13:33