Standard +0.3 This is a straightforward matrix algebra manipulation requiring knowledge that (AB)^(-1) = B^(-1)A^(-1) and that matrices can be cancelled when non-singular. The question tests basic properties of matrix inverses with minimal steps, making it slightly easier than average even for Further Maths, though the inverse property itself elevates it slightly above pure recall.
4 Given that \(\mathbf { A }\) and \(\mathbf { B }\) are \(2 \times 2\) non-singular matrices and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix, simplify
$$\mathbf { B } ( \mathbf { A B } ) ^ { - 1 } \mathbf { A } - \mathbf { I } .$$
4 Given that $\mathbf { A }$ and $\mathbf { B }$ are $2 \times 2$ non-singular matrices and $\mathbf { I }$ is the $2 \times 2$ identity matrix, simplify
$$\mathbf { B } ( \mathbf { A B } ) ^ { - 1 } \mathbf { A } - \mathbf { I } .$$
\hfill \mbox{\textit{OCR FP1 2009 Q4 [4]}}