MathNet 2019-part-05 — 184 problems (EN–VI) Question 109

Let $A$, $B \in \mathcal{M}_n(\mathbb{C})$ and $c \in \mathbb{C}^*$ so that $AB - BA = c \cdot (A - B)$. Prove that the matrices $A$ and $B$ have the same eigenvalues.