Let G be a Finite group written mlutiplicatively. Prove that if the order of G is odd, then every $\displaystyle x \in G$ has a square root. Conclude the proof with there exists exactly one $\displaystyle g \in G$ with $\displaystyle g^2=x$

I think i need to show that squaring is an injective funciton from $\displaystyle G \to G$ and use the pigeonhole principle...