Determinant of $\left[\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right]$

Calculate $\left|\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right|$.

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

$\left|\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right| = \left(1 - \lambda\right)\cdot \left(3 - \lambda\right) - \left(2\right)\cdot \left(0\right) = \lambda^{2} - 4 \lambda + 3$

$\left|\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right| = \left(\lambda - 3\right) \left(\lambda - 1\right)$A