Solution PEE.T10 Robert Beezer

Suppose that the characteristic polynomial of $A$ is \begin{equation*} \charpoly{A}{x}=a_0+a_1x+a_2x^2+\dots+a_nx^n \end{equation*} Then \begin{align*} a_0 &=a_0+a_1(0)+a_2(0)^2+\dots+a_n(0)^n\\ &=\charpoly{A}{0}\\ &=\detname{A-0I_n} &&\knowl{./knowls/definition.CP.knowl}{\text{Definition CP}}\\ &=\detname{A} \end{align*}