Determinant of $$$\left[\begin{array}{cc}2 - \lambda & 5\\-2 & - \lambda - 4\end{array}\right]$$$

Calculate $$$\left|\begin{array}{cc}2 - \lambda & 5\\-2 & - \lambda - 4\end{array}\right|$$$.

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

$$$\left|\begin{array}{cc}2 - \lambda & 5\\-2 & - \lambda - 4\end{array}\right| = \left(2 - \lambda\right)\cdot \left(- \lambda - 4\right) - \left(5\right)\cdot \left(-2\right) = \lambda^{2} + 2 \lambda + 2$$$

$$$\left|\begin{array}{cc}2 - \lambda & 5\\-2 & - \lambda - 4\end{array}\right| = \lambda^{2} + 2 \lambda + 2$$$A