BALTIC-WAY 2016 Problem 8

Find all real numbers a for which there exists a non-constant function $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying the following two equations for all $x \in \mathbb{R}$ : i) $f(a x)=a^{2} f(x)$ and

ii) $f(f(x))=a f(x)$.