Show whether the function $\phi(x)=21x \bmod 36$ is one-to-one and/or onto

Question

Let $\phi: \mathbb{Z}_{36} \rightarrow \mathbb{Z}_{36}$ and define $\phi(x)=21x\bmod36$.

I have already shown that the function is a homomorphism. I am having trouble showing whether it is one-to-one and/or onto.

So far I have for one-to-one:

Let $x_1, x_2 \in \mathbb{Z}_{36}$ and let $\phi(x_1)=\phi(x_2)$. Then $21x_1\bmod36$ = $21x_2\bmod36$. I am unsure where to go from here.

Answer 1

You can't prove it because it is false. Note that $\phi(0)=\phi(12)$, but $0\neq12$. And it is not surjective.