linear algebra - Finding the eigenvalues of a matrix problem

So I do know how to compute the eigenvalues of a matrix. At least, that's what I thought. I got the matrix

A =

$$\begin{bmatrix}1&-2&0\\-2&0&2\\0&2&-1\end{bmatrix}$$

My approach is by finding the determinant:

$$\begin{equation} \text{det}\left(A-\lambda In\right) = 0 \end{equation}$$

so it becomes

$$\text{det}\left( \begin{bmatrix}1-\lambda&-2&0\\-2&0&2\\0&2&-1-\lambda\end{bmatrix} \right) = 0.$$
But this gave me 8 lambda

According to calculators, it should give me -3, 3 and 0
What did I miss?