grandes-ecoles 2022 Q1

grandes-ecoles · France · mines-ponts-maths2__mp Matrices Matrix Algebra and Product Properties
We are given two matrices $A$ and $B$ in $\mathcal{M}_n(\mathbf{K})$. We assume that $A$ and $B$ commute.
$\mathbf{1}$ ▷ Show that the matrices $A$ and $e^{B}$ commute.
We are given two matrices $A$ and $B$ in $\mathcal{M}_n(\mathbf{K})$. We assume that $A$ and $B$ commute.

$\mathbf{1}$ ▷ Show that the matrices $A$ and $e^{B}$ commute.