I'm studying analytic number theory for undergraduates and I read this theorem in Tom Apostol's book on the second chapter:
Theorem 2.12. If $f$ is multiplicative then $f(1)=1$
And under need there is a note that says that $\Lambda (n)$ is not multiplicative because $\Lambda (1) = 0$. So I wonder if the converse of the theorem is true.