Let $E$ be a $\mathbb{C}$-vector space of dimension $n \geq 1$. Study whether the equivalence of the previous question holds when we replace the hypothesis $u^2 = \operatorname{Id}_E$ by $u^k = \operatorname{Id}_E$ for $k = 3$, then for $k = 4$.
Let $E$ be a $\mathbb{C}$-vector space of dimension $n \geq 1$. Study whether the equivalence of the previous question holds when we replace the hypothesis $u^2 = \operatorname{Id}_E$ by $u^k = \operatorname{Id}_E$ for $k = 3$, then for $k = 4$.