Given that the characteristic polynomial of $\displaystyle A$ is $\displaystyle t^4 + t + 1$. How would I go about calculating the characteristic polynomial of $\displaystyle A^2$?

I originally thought of using the fact that the eigenvalues of $\displaystyle A^2$ would simply be the square of the eigen values of $\displaystyle A$. But unfortunately I couldnt calculate the eigenvalues of A.

Any help would be great, thanks!