MathNet 2011 Question 8

Let $A$ be a finite set of positive reals, let $B = \{\frac{x}{y}: x, y \in A\}$ and let $C = \{xy: x, y \in A\}$. If we denote $cardX = |X|$, show that: $|A| \cdot |B| \le |C|^2$.