Challenging +1.2 This is a Further Maths question requiring knowledge of the Cayley-Hamilton theorem and matrix inversion through it. While the theorem itself is advanced, the application is mechanical: find the characteristic polynomial, substitute A, rearrange to isolate A^{-1}. The 3×3 matrix requires careful arithmetic but follows a standard procedure with no novel insight needed. Slightly above average difficulty due to the Further Maths content and computational demands.
The matrix A is $\begin{pmatrix} -1 & 2 & 4 \\ 0 & -1 & -25 \\ -3 & 5 & -1 \end{pmatrix}$.
Use the Cayley-Hamilton theorem to find A$^{-1}$. [8]
\hfill \mbox{\textit{OCR MEI Further Extra Pure 2019 Q3 [8]}}