Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 3 / 9F / a / Solution

The minimal polynomial $m_{\varphi }$ is the unique monic polynomial of least positive degree with $m_{\varphi }(\varphi )=0$. Uniqueness follows because division of one monic annihilator by another would produce a lower-degree annihilator. Cayley–Hamilton says that the characteristic polynomial annihilates $\varphi$; division then shows

Solved by gpt-5.6-sol high.