Determinant of $$$\left[\begin{array}{cc}1 - \lambda & 1 - i\\1 + i & - \lambda\end{array}\right]$$$

Calculate $$$\left|\begin{array}{cc}1 - \lambda & 1 - i\\1 + i & - \lambda\end{array}\right|$$$.

The determinant of a 2x2 matrix is $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}1 - \lambda & 1 - i\\1 + i & - \lambda\end{array}\right| = \left(1 - \lambda\right)\cdot \left(- \lambda\right) - \left(1 - i\right)\cdot \left(1 + i\right) = \lambda^{2} - \lambda - 2$$$

$$$\left|\begin{array}{cc}1 - \lambda & 1 - i\\1 + i & - \lambda\end{array}\right| = \left(\lambda - 2\right) \left(\lambda + 1\right)$$$A