Idiotic determinant mistake?

Question

I need to calculate $$\begin{vmatrix} \lambda & -1 & 0 & 0\\ -1 & \lambda & 0 & 0 \\ 0 & 0 & \lambda & -1 \\ 0 & 0 & -1 & \lambda \end{vmatrix}.$$

For the life of me I don't see what my mistake is: expanding in the first row we have $$\lambda^2(\lambda ^2-1)-(-1)(-1)(\lambda ^2-1)= (\lambda^2-1)^2 .$$ What is my error?

Answer 1

As everyone comments, my answer is correct.