After these next two, I'm done for the semester! Thanks to all!

(1) Let $\displaystyle f$ be a multiplicative function. Prove that

$\displaystyle \sum_{d|n}\mu(d)f(d) = \prod_{p|n}(1-f(p))$

(2) Let $\displaystyle f$ and $\displaystyle g$ be arithmetic functions with $\displaystyle g(n)\in \mathbb{R}^+$ and $\displaystyle f(n)= \prod_{d|n}g(d).$ for all $\displaystyle n \in \mathbb{Z}^+$.

Prove that $\displaystyle g(n)= \prod_{d|n}f(d)^{\mu\left(\frac{n}{d}\right)}$ for all $\displaystyle n \in \mathbb{Z}^+$

Thanks! I'm working on these last two and I am freeee for the summer