Find the matrix that represents a reflection in the line \(y = - x\).
The matrix \(\mathbf { C }\) is given by \(\mathbf { C } = \left( \begin{array} { l l } 1 & 0 0 & 4 \end{array} \right)\).
Describe fully the geometrical transformation represented by \(\mathbf { C }\).
State the value of the determinant of \(\mathbf { C }\) and describe briefly how this value relates to the transformation represented by \(\mathbf { C }\).