What is the minimal polynomial of $A$?
$$A=\left[\begin{matrix} 0&0&c\\ 1&0&b\\ 0&1&a \end{matrix}\right]$$
I tried to classify each case of eigenvalues and match them with a characteristic polynomial (3 equal, 2 equal and all different), but this became far too complicated.
Is there a simpler way?
(Sorry for my poor english.)