Chapter 3.3, Problem 27E

Let S be the parallelogram determined by the vectors ${\text{b}}_{\text{1}}=\left[\begin{array}{c}-2\\ 3\end{array}\right]$ and ${\text{b}}_{\text{2}}=\left[\begin{array}{c}-2\\ 5\end{array}\right]$, and let $A=\left[\begin{array}{cc}6& -3\\ -3& 2\end{array}\right]$ Compute the area of the image of S under the mapping $\text{x }\mapsto A\text{x}\text{.}$