Soit \(f \in \mathcal{L}(E)\) tel que \(f^3 = \mathrm{id}_E\).
1
Montrer que \(\mathrm{Ker}(f-\mathrm{id}) \oplus \Im(f-\mathrm{id}) = E\).
2
Montrer que \(\mathrm{Ker}(f-\mathrm{id}) = \Im(f^2 + f + \mathrm{id})\) et \(\mathrm{Im}(f-\mathrm{id}) = \mathrm{Ker}(f^2 + f + \mathrm{id})\).