$\mathbf{3}$ ▷ Conversely, suppose the relation $\forall t \in \mathbf{R} \quad e^{t(A+B)} = e^{tA} e^{tB}$ is satisfied. By differentiating this relation twice with respect to the real variable $t$, show that the matrices $A$ and $B$ commute.
$\mathbf{3}$ ▷ Conversely, suppose the relation $\forall t \in \mathbf{R} \quad e^{t(A+B)} = e^{tA} e^{tB}$ is satisfied. By differentiating this relation twice with respect to the real variable $t$, show that the matrices $A$ and $B$ commute.