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?