Prove or disprove $ab\mid ac\Longrightarrow b\mid c$ I need to prove or to give a counter-example:

$$ab\mid ac\Longrightarrow b\mid c$$

My attempt:
Yes, this is correct, let's divide $ab$ and $ac$ by $a$ (assuming that $a\neq 0$) we get $$b\mid c$$ and that's it.
Is my attempt correct?

Yes. Your attempt is correct. Let me simplify it.
Proof:
Assuming $a$ is not 0.
$$ab|ac \implies kab = ac \implies kb = c \implies b|c$$
