Hello, I need help with the following problem

Let $\displaystyle n \in \mathbb{N}$ and $\displaystyle a \in \mathbb{Z}$, so $\displaystyle [a] \in \mathbb{Z}_n$. Prove that there exists an integer $\displaystyle b$ such that $\displaystyle [a][b]=[1]$ if and only if $\displaystyle gcd(a,n)=1$.