6 The matrix \(\mathbf { A }\) is given by \(\left( \begin{array} { l l } 1 & 2
1 & a \end{array} \right)\) and the matrix \(\mathbf { B }\) is given by \(\left( \begin{array} { c c } 2 & 1
- 1 & b \end{array} \right)\).
- Find the matrix \(\mathbf { A B }\).
- State the conditions on \(a\) and \(b\) for \(\mathbf { A B }\) to be a singular matrix.
\(P Q R S\) is a quadrilateral and the vertices \(P , Q , R\) and \(S\) are in clockwise order. A transformation, T , is represented by the matrix \(\mathbf { A B }\). - State the effect on both the area and also the orientation of the image of \(P Q R S\) under T in each of the following cases.
(a) \(\quad a = 1\) and \(b = 1\)
(b) \(\quad a = 2\) and \(b = 3\)