Standard +0.3 This is a Further Maths matrix equation requiring algebraic manipulation to isolate A. The key insight is to rearrange AB = I + 2A into A(B - 2I) = I, then find A = (B - 2I)^{-1}. While it requires understanding matrix algebra and computing a 2×2 inverse, these are standard FM techniques with straightforward calculation, making it slightly easier than average.
Two matrices \(\mathbf{A}\) and \(\mathbf{B}\) satisfy the equation
$$\mathbf{AB} = I + 2\mathbf{A}$$
where \(I\) is the identity matrix and \(\mathbf{B} = \begin{pmatrix} 3 & -2 \\ -4 & 8 \end{pmatrix}\)
Find \(\mathbf{A}\).
[3 marks]
Two matrices $\mathbf{A}$ and $\mathbf{B}$ satisfy the equation
$$\mathbf{AB} = I + 2\mathbf{A}$$
where $I$ is the identity matrix and $\mathbf{B} = \begin{pmatrix} 3 & -2 \\ -4 & 8 \end{pmatrix}$
Find $\mathbf{A}$.
[3 marks]
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q5 [3]}}