Solution
= Solution
This assertion is false in general. In dimension two take $A=\begin{pmatrix}1&0\\0&0\end{pmatrix}$, $B=\begin{pmatrix}0&1\\0&0\end{pmatrix}$ and $C=\begin{pmatrix}0&0\\1&0\end{pmatrix}$. Then $ABC=A$, whereas $ACB=0$. Their <characteristic polynomials> are $\lambda(\lambda-1)$ and $\lambda^2$, respectively, so $\boxed{p_{ABC}\ne p_{ACB}}$.