Standard +0.3 This is a straightforward 3×3 matrix inversion problem from Further Pure 1, requiring systematic application of the cofactor method or row reduction. While it involves more computation than a 2×2 inverse, it's a standard textbook exercise with no conceptual challenges beyond careful arithmetic. The parameter 'a' adds minimal complexity since the method remains routine.
6 The matrix \(\mathbf { C }\) is given by \(\mathbf { C } = \left( \begin{array} { r r r } a & 1 & 0 \\ 1 & 2 & 1 \\ - 1 & 3 & 4 \end{array} \right)\), where \(a \neq 1\). Find \(\mathbf { C } ^ { - 1 }\).