Question 4
Let $n \ge 2$ be an integer and $a$ and $b$ complex numbers such that $a \neq 0$ and $b^k \neq 1$, for any $k \in \{1, 2, \dots, n\}$. Suppose that the matrices $A, B \in \mathcal{M}_n(\mathbb{C})$ are such that $BA = aI_n + bAB$. Prove that $A$ and $B$ are invertible.
Sorin Rădulescu and Mihai Piticari
Sorin Rădulescu and Mihai Piticari