## Prove or disprove the folllowing:

Let $A$ and $B$ be two matrices, of order $m$x $n$ and $n$x $m$ respectively, such that $r(AB) = r(BA)= min\{r(A), r(B)\}$. Then $AB$ is idempotent implies $BA$ is also idempotent.

Please help. I am neither able to prove this, nor able to get any counter-example to disprove this.