Let $B \in \mathbf{M}_n$ be a diagonalizable matrix. We assume that the characteristic polynomial of $B$ is reciprocal or antireciprocal. Prove that $B$ is invertible and similar to its inverse.
Let $B \in \mathbf{M}_n$ be a diagonalizable matrix. We assume that the characteristic polynomial of $B$ is reciprocal or antireciprocal. Prove that $B$ is invertible and similar to its inverse.