Divisibility transitive proof

Question

For all integers $a$, $b$, $c$:

If $a \mid b$ and $b \mid c$ then $a \mid c$.

For all integers $a$ and $b$:

If $a \mid b$ and $b \mid a$ then $a = b$.

I am lost as to how to start this and complete it.

Answer 1

Hint: for the first one, write $b=pa$ and $c=qb$ then $c = (pq)a$. For the second one, note that $a \mid b \ne 0 \implies |a| \le |b|\,$, then consider the case of signed vs. unsigned integers.