pow:problem6s21 [Binghamton University Department of Mathematics and Statistics]

Problem 6 (due Monday, May 10)

Let $A$ and $B$ be square matrices of the same size such that $A^{2020}=I=B^{2020}$ and $AB=-BA$. Prove that $I+A+B$ is invertible. (Here $I$ is the identity matrix).

No solutions were submitted. For a detailed solution see the following link Solution.