es un número racional.

Question

Deje que <span class="math-container">$A \in \mathcal{M}_3(\mathbb{C})$</span> de tal forma que <span class="math-container">$\mathrm{tr}(A^2) = \mathrm{tr}(A^3) \in \mathbb{Q},$</span> donde <span class="math-container">$\mathrm{tr}(A)$</span> es el rastro de <span class="math-container">$A.$</span> Es posible probar que <span class="math-container">$\mathrm{tr}(A^4) \in \mathbb{Q}?$</span>