[Math] Prove that if $a\equiv b \pmod n$ then $ra\equiv rb \pmod n$

Question

I seem to not be able to find anything about these type of questions, could anyone help me prove the following question. Start up on how to do the question would be appreciated too!

$a \equiv b \pmod n$, then $ra \equiv rb \pmod n$,

Thanks in advance.

Answer 1

$a \equiv b \pmod{n} \iff n|(a-b)$. Knowing this, then certainly $n|r(a-b)$.

Hence, $n|(ra-rb) \iff ra \equiv rb \pmod{n}$.