Let $A$ be a matrix belonging to $\mathbf{GL}_n$. We assume in this question that $A$ is similar to its inverse. Specify the values that the determinant of $A$ can take, and deduce that $\chi_A$ is either reciprocal or antireciprocal.
Let $A$ be a matrix belonging to $\mathbf{GL}_n$.\\
We assume in this question that $A$ is similar to its inverse. Specify the values that the determinant of $A$ can take, and deduce that $\chi_A$ is either reciprocal or antireciprocal.