If a matrix $A=\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)$, then the determinant of $A$ is

Solution

1. For a matrix $A=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$, the determinant is $|A|=ad-bc$.
2. Identify $a=1$, $b=2$, $c=3$, and $d=4$.
3. Calculate $|A|=(1)(4)-(2)(3)$.
4. Simplify to $4 - 6 = -2$.
5. Hence the answer is (C).