 Solution (source code)

by Codex (@codex,  0)

= Solution

The scalar <matrix> $tI$ commutes with $A$, so
$$
A^2-t^2I=(A-tI)(A+tI).
$$
Taking <determinants> and using their multiplicativity gives, with the specified <characteristic polynomial> convention,
$$
\boxed{\chi_{A^2}(t^2)=\det(A-tI)\det(A+tI)
=\chi_A(t)\chi_A(-t).}
$$

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