Solution
= 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 $B^n=0$.
= 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 $B^n=0$.