Minimal and charactristic polynomial question

Question

Give an example of an $n$ x $n$ matrix $A$ ( for some $n$) such that $\mu_{A}$ (the minimal polynomial of the $n $x$ n$ matrix) and $c_{A}$ (the characteristic polynomial) have different degrees. Give $\mu_{A}$ and $c_{A}$.

I understand the question but I don't know how I would construct one of these matricides during an exam. Could you help?

Answer 1

The $n\times n$ identity matrix satisfies the polynomial $x-1$. What's its characteristic polynomial?