Problem of March 03 2019


Problem. Let $A$ be a $n\times n$ complex matrix such that $(A’)^m=A^k$, where $A’$ stands for the transpose of $A$ and $m,k$ are distinct positive integers. Prove that the eigenvalues of $A$ are zero or root of unity ( $\xi^\ell =1$ for some positive integer $\ell$).

Please feel free to post your solutions.

 

Linearity

This website is supposed to help you study Linear Algebras. Please only read these solutions after thinking about the problems carefully. Do not just copy these solutions.

Leave a Reply

Your email address will not be published. Required fields are marked *