If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.

I'm wondering if you can help me with this one? 


Question: What is the probability that Brian makes money on his first roll
Answer: Nine cases have them both odd. Nine have them both even.
So you only have the other 18 to check.
And they come in pairs, as $(2,5)$ is the same as $(5,2)$, so you only have nine cases to check.