Solution
= Solution
The <characteristic polynomial>, using the convention $\det(\lambda I-A)$, is
$$
p(\lambda)=\lambda^3+\lambda^2-21\lambda-45
=(\lambda-5)(\lambda+3)^2.
$$
Its zeros give the <eigenvalues>, including <algebraic multiplicity>:
$$
\boxed{5,\qquad-3,\qquad-3}.
$$
Their product is $45$ and their sum is $-1$, agreeing with the <determinant> and <trace> of the <matrix>.