Determinant of $$$\left[\begin{array}{cc}2 t & 3 t^{2}\\2 & 6 t\end{array}\right]$$$

Calculate $$$\left|\begin{array}{cc}2 t & 3 t^{2}\\2 & 6 t\end{array}\right|$$$.

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

$$$\left|\begin{array}{cc}2 t & 3 t^{2}\\2 & 6 t\end{array}\right| = \left(2 t\right)\cdot \left(6 t\right) - \left(3 t^{2}\right)\cdot \left(2\right) = 6 t^{2}$$$

$$$\left|\begin{array}{cc}2 t & 3 t^{2}\\2 & 6 t\end{array}\right| = 6 t^{2}$$$A