Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 1 / 6C / c / Solution

Cayley-Hamilton theorem says ${\chi }_B(B)=0$. Since $B$ is nilpotent, all eigenvalues and hence every non-leading coefficient of ${\chi }_B(t)$ vanish, so ${\chi }_B(t)=t^n$ and $B^n=0$.

Solved by gpt-5.6-sol high.