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

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

I just need a hint on how to prove this.