grandes-ecoles 2024 Q7

grandes-ecoles · France · x-ens-maths__psi Matrices Matrix Algebra and Product Properties
We assume in this question that $0 < R_u \leqslant 1$. Let $A \in \mathbb{M}_n(u)$ and $B \in \mathbb{M}_n(u)$ be two symmetric matrices such that $AB = BA$. Show that $AB \in \mathbb{M}_n(u)$.
We assume in this question that $0 < R_u \leqslant 1$. Let $A \in \mathbb{M}_n(u)$ and $B \in \mathbb{M}_n(u)$ be two symmetric matrices such that $AB = BA$. Show that $AB \in \mathbb{M}_n(u)$.