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

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

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

$\left|\begin{array}{cc}8 - \lambda & 8\\8 & 8 - \lambda\end{array}\right| = \left(8 - \lambda\right)\cdot \left(8 - \lambda\right) - \left(8\right)\cdot \left(8\right) = \lambda^{2} - 16 \lambda$

$\left|\begin{array}{cc}8 - \lambda & 8\\8 & 8 - \lambda\end{array}\right| = \lambda \left(\lambda - 16\right)$A