Z modulo n/Representatives/Associativity and group/Exercise

Let ${\displaystyle {}d\in \mathbb {N} _{+}}$, and consider on

${\displaystyle {}\mathbb {Z} /(d)=\{0,1,\ldots ,d-1\}\,}$

the operation

${\displaystyle {}a+b:=(a+b)\mod d={\begin{cases}a+b,{\text{ if }}a+b<d\,,\\a+b-d,{\text{ if }}a+b\geq d\,.\end{cases}}\,}$

Show that this defines an associative operation on this set. Moreover, show that this is even a group.