## Multiplication of residue classes of integers is associative

Prove that multiplication of residue classes in $\mathbb{Z}/(n)$ is associative. (You may assume that it is well defined.)

We have

 $(\overline{a} \cdot \overline{b}) \cdot \overline{c}$ = $\overline{a \cdot b} \cdot \overline{c}$ = $\overline{(a \cdot b) \cdot c}$ = $\overline{a \cdot (b \cdot c)}$ = $\overline{a} \cdot \overline{b \cdot c}$ = $\overline{a} \cdot (\overline{b} \cdot \overline{c})$,

since integer multiplication is associative.