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Let $A$ be an element of $\mathrm{M}_{4}(\mathbb{R})$ with characteristic polynomial $t^{4}-t$. What is the characteristic polynomial of $A^{2}$ ?

1. $t^{4}-t$
2. $t^{4}-2 t^{3}+t^{2}$
3. $t^{4}-t^{2}$
4. None of the other three options