Conditions for a C*-algebra to be Abelian

Question

Please help me with this problem. I don't know how to get into proof.

Let $A$ be a $C^*$-Algebra. Show that if the condition $0 \leq x \leq y,~~ x,y\in A,$ implies $x^2 \leq y^2,$ then $A$ is abelian.