1 The matrix \(\mathbf { M }\) is given by \(\mathbf { M } = \left( \begin{array} { l l } 1 & b
0 & 1 \end{array} \right) \left( \begin{array} { l l } a & 0
0 & 1 \end{array} \right)\), where \(a\) and \(b\) are positive constants.

1. The matrix \(\mathbf { M }\) represents a sequence of two geometrical transformations. State the type of each transformation, and make clear the order in which they are applied.
   The unit square in the \(x - y\) plane is transformed by \(\mathbf { M }\) onto parallelogram \(O P Q R\).
2. Find, in terms of \(a\) and \(b\), the matrix which transforms parallelogram \(O P Q R\) onto the unit square.
   It is given that the area of \(O P Q R\) is \(2 \mathrm {~cm} ^ { 2 }\) and that the line \(\mathrm { x } + 3 \mathrm { y } = 0\) is invariant under the transformation represented by \(\mathbf { M }\).
3. Find the values of \(a\) and \(b\).