I am trying to find the determinant of this matrix with eigenvalues in it.
$(\lambda I - A)$ = $\begin{bmatrix} \lambda - 1 & 3 & 0 \\ 3 & \lambda - 1 & 0 \\ 0 & 0 & \lambda + 2 \\ \end{bmatrix}$
$det(A)= (\lambda - 1) \begin{vmatrix} \lambda - 1 & 0 \\ 0 & \lambda + 2 \\ \end{vmatrix}$- $3\begin{vmatrix} 3 & 0 \\ 0 & \lambda + 2 \\ \end{vmatrix}$ + $0\begin{vmatrix} 3 & \lambda - 1 \\ 0 & 0 \\ \end{vmatrix}$
Stuck here. This is the correct factorization, but what do the [] mean?
= $[(\lambda - 1)^2 - 9](\lambda + 2)$
= $(\lambda - 4)(\lambda + 2)^2$