Endomorphism/R^2/No eigenvalue, power has/Example/Exercise

Give an example of a linear mapping

$\varphi \colon \mathbb {R} ^{2}\longrightarrow \mathbb {R} ^{2}$

such that ${}\varphi$ has no eigenvalue, but a certain power ${}\varphi ^{n}$, ${}n\geq 2$, has an eigenvalue.

Create a solution