Characteristic equation is $ | A- \lambda I | = 0 $
(1)$$\begin{vmatrix}1- \lambda & 0\\
0 & - \lambda\\
\end{vmatrix} = 0$$$ (1- \lambda )(- \lambda) = 0 $
$\implies \lambda =0,1 $
Similarly, (2) $ \lambda =0,0 $
(3) $ \lambda \neq 1 $
(4) $ \lambda =-1,-1 $
Therefore, Answer is (A) one