6.
$$\mathbf { A } = \left( \begin{array} { r r }
0 & 1
- 1 & 0
\end{array} \right) , \quad \mathbf { B } = \left( \begin{array} { l l }
2 & 3
1 & 4
\end{array} \right)$$
The transformation represented by \(\mathbf { B }\) followed by the transformation represented by \(\mathbf { A }\) is equivalent to the transformation represented by \(\mathbf { P }\).
- Find the matrix \(\mathbf { P }\).
Triangle \(T\) is transformed to the triangle \(T ^ { \prime }\) by the transformation represented by \(\mathbf { P }\).
Given that the area of triangle \(T ^ { \prime }\) is 24 square units,
- find the area of triangle \(T\).
Triangle \(T ^ { \prime }\) is transformed to the original triangle \(T\) by the matrix represented by \(\mathbf { Q }\).
- Find the matrix \(\mathbf { Q }\).