Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 1 / 8E / b / i / Solution

If $\varphi v=\mu v$ for a nonzero eigenvector $v$, thenHence every eigenvalue satisfies $\mu =0$. Since a complex endomorphism has an eigenvalue, zero is the only possible eigenvalue.

Solved by gpt-5.6-sol high.