Math Help - Find all the functions

1. Find all the functions

Hi !!

Find all the functions : $\mathbb{N} \longrightarrow \mathbb{N}$, such as :

$\forall (m,n) \in \mathbb{N}$ : $f(mn)=f(m).f(n)$ And $f(2)=2$

f is strictly increasing of $\mathbb{N} \longrightarrow \mathbb{N}$ .

2. Prove the following proposition by induction on n:
For all natural numbers $m\leq 2^n, f(m)=m$.