1 Determinant of a 2 $\times$ 2 matrix

The determinant of the matrix $A=\left[\begin{array}{cc}\hfill a\hfill & \hfill b\hfill \\ \hfill c\hfill & \hfill d\hfill \end{array}\right]$ is denoted by $\left|\begin{array}{cc}\hfill a\hfill & \hfill b\hfill \\ \hfill c\hfill & \hfill d\hfill \end{array}\right|$ (note the change from square brackets to vertical lines) and is defined to be the number $ad-bc$ . That is:

$\left|\begin{array}{cc}\hfill a\hfill & \hfill b\hfill \\ \hfill c\hfill & \hfill d\hfill \end{array}\right|=ad-bc$

We can use the notation det $\left(A\right)$ or $\mid A\mid$ or $\Delta$ to denote the determinant of $A$ .

Task!

Find the determinants of the matrices

$A=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 3\hfill & \hfill 4\hfill \end{array}\right],B=\left[\begin{array}{cc}\hfill 4& \hfill -1\\ \hfill -2& \hfill -3\end{array}\right],C=\left[\begin{array}{cc}\hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill \end{array}\right]D=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill 2\hfill & \hfill 3\hfill \end{array}\right],$

$E=\left[\begin{array}{cc}\hfill 2\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 4\hfill \end{array}\right],F=\left[\begin{array}{cc}\hfill -1& \hfill 0\\ \hfill 0& \hfill -3\end{array}\right],G=\left[\begin{array}{cc}\hfill 1& \hfill 2\\ \hfill -2& \hfill -4\end{array}\right].$

Answer