Answer
See below.
Work Step by Step
(a) To prove the statement by contraposition, we need to prove "for any integer $a,b,c$, if $a|b$, then $a|bc$". To prove, let $b=ka$ ($k$ is an integer), we have $bc=kac=(kc)a$ which leads to $a|bc$. Thus we proved the statement by contraposition.
(b) To prove the statement by contradiction, suppose "there exist integers $a,b,c$, such that $a\nmid bc$, and $a|b$". Let $b=ka$ ($k$ is an integer), we have $bc=kac=(kc)a$ which leads to $a|bc$ in contradiction witth the condition $a\nmid bc$. Thus, we proved the statement by contradiction.
