Guaranteed for all vector spaces $V,W$.

Identity Transformation

$I:V\to V$ given by $I(v)=v$

Proof

Check that $I$ is linear

We want to check $I((a⊡\overrightarrow{u})⊞(b⊡\overrightarrow{v}))=(a⊡\overrightarrow{u})⊞(b⊡\overrightarrow{v})$ by defn of $I$ $=(a⊡I(\overrightarrow{u}))⊞(b⊡I(\overrightarrow{v}))$ by defn of $I$ Therefore, $I:(v,⊞,⊡)\to (v,⊞,⊡)$ is linear