Showing a nonzero multiplicative arithmetic function satisfies $f(1) = 1$

Question

let $f$ be multiplicative arithmetic function. if there exist a positive integer $n$ such that $f(n)$ is not equal to $0$ (so $f$ is not identically zero) prove that $f(1)=1$. I got that $gcd(1,n)=1$ and since $f$ is multiplicative then $f(n.1)=f(n)f(1)$. I do not know how to proceed further. Any help is appreciated Thank you.