Question

what is the characteristic equation of the matrix \[\left[\begin{matrix}1&0&-1\\0&2&0\\1&0&1\end{matrix}\right]\]
Please, help

Answer 1

I got \(r^3 -4r^2+6r-4 =0\) is it correct?

Answer 2

Just subtract an arbitrary r in the elements of the main diagonal then find the determinant

Answer 3

another form is (r-2)(r^2 - 2r +2) =0 is it correct? I would like to know the answer.