Determinant of $$$\left[\begin{array}{cc}8 - \lambda & 12\\12 & 26 - \lambda\end{array}\right]$$$

Calculate $$$\left|\begin{array}{cc}8 - \lambda & 12\\12 & 26 - \lambda\end{array}\right|$$$.

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

$$$\left|\begin{array}{cc}8 - \lambda & 12\\12 & 26 - \lambda\end{array}\right| = \left(8 - \lambda\right)\cdot \left(26 - \lambda\right) - \left(12\right)\cdot \left(12\right) = \lambda^{2} - 34 \lambda + 64$$$

$$$\left|\begin{array}{cc}8 - \lambda & 12\\12 & 26 - \lambda\end{array}\right| = \left(\lambda - 32\right) \left(\lambda - 2\right)$$$A