Determinant of $\left[\begin{array}{cc}4 & 5\\7 & 8\end{array}\right]$

Calculate $\left|\begin{array}{cc}4 & 5\\7 & 8\end{array}\right|$.

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

$\left|\begin{array}{cc}4 & 5\\7 & 8\end{array}\right| = \left(4\right)\cdot \left(8\right) - \left(5\right)\cdot \left(7\right) = -3$

$\left|\begin{array}{cc}4 & 5\\7 & 8\end{array}\right| = -3$A