Prove that your answer is correct. $a|b$ if and only if $ac|bc$.

Question

Now i know this much: If we take this in the forward direction that is if $a|b$ then $ac|bc$ then we can say that since $b = ak$ where $k$ is some integer, then $ac|ack$ which is true for all integer k. Now for the backward direction, we have $ac|bc$ and $bc = ack$ which becomes $b = ak$ and hence $a|ak$ which is again true for all integers. Is my proof correct?