How can I prove that tr($\rho^2) $ = 1 only and only when the state is pure  ? 

My idea: 
I know how to show that tr($\rho^2) \leq$ 1 and from there I am trying to show by contradiction that tr($\rho^2) $ = 1 can only but true for pure states  but I am kind of stuck. 

I just need a hint on how to prove this.