The CharacteristicMatrix(A, t) command constructs the characteristic Matrix $M=-t\mathrm{Id}+A$, where Id is the appropriately sized identity Matrix. The determinant of M, found by using $\mathrm{Determinant}\left(M\right)$, is the characteristic polynomial of A.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$A≔⟨⟨1\,2\,3⟩\left|⟨1\,2\,3⟩\right|⟨1\,5\,6⟩⟩$

$A≔\left[\begin{array}{ccc}1& 1& 1\\ 2& 2& 5\\ 3& 3& 6\end{array}\right]$

$C≔\mathrm{CharacteristicMatrix}\left(A\,t\right)$

$C≔\left[\begin{array}{ccc}t-1& \mathrm{-1}& \mathrm{-1}\\ \mathrm{-2}& t-2& \mathrm{-5}\\ \mathrm{-3}& \mathrm{-3}& t-6\end{array}\right]$

$\mathrm{Determinant}\left(C\right)$

$t^3-9t^2$

$\mathrm{CharacteristicPolynomial}\left(A\,t\right)$

$t^3-9t^2$