Is it true, If $A$ is turing recognizable and $A \leq_m\bar{A}$ then $A$ is recursive? If $A$ is turing recognizable and $A \leq_m\bar{A}$ then $A$ is recursive? 
If it is true how to prove it?

Update

It is my attempt, If $A$ is turing recognizable (r.e.) and $\bar{A}$ is r.e. then $A$ is recursive. but by $A \leq_m\bar{A}$ I can't deduce that $\bar{A}$ is r.e.
Hint: If $A$ reduces to $\overline{A}$ then $\overline{A}$ reduces to $A$ (using the same reduction).