Answer
$\text{determinant of }
\begin{bmatrix}
6 & 9
\\
3 & 6
\end{bmatrix}
=
9$
Work Step by Step
Using the determinant of a $2\times2$ matrix $A=\begin{bmatrix}a&b\\c&d
\end{bmatrix}$ which is given by $ad-cb$ the determinant of the given matrix, $
\begin{bmatrix}
6 & 9
\\
3 & 6
\end{bmatrix}
,$ is
\begin{align*}
&
6(6)-3(9)
\\&=
36-27
\\&=
9
.\end{align*}
Hence, the $
\text{determinant of }
\begin{bmatrix}
6 & 9
\\
3 & 6
\end{bmatrix}
=
9
.$
