elementary number theory - Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = pm b$

Let $a$ and $b$ be nonzero integers. Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$.

Since this is a iff statement, I need to prove it both ways:

$\Rightarrow$ If $a=\pm b$, then $a$ divides $b$ and $b$ divides $a$; and

$\Leftarrow$ If $a$ divides $b$ and $b$ divides $a$, then $a=\pm b$.

I tried to prove it but I don't know how to manage the $\pm$ sign, can anyone give me a hit or suggestion to start this proof?

Thanks