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

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

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

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

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