IAL 2025 May FP1 Q1

Question

[!problem]

The matrix $M$ is given by

$M = \begin{pmatrix} 1 & a \\ 3 & -5 \end{pmatrix}$

where $a$ is a constant, $a \neq -\frac{5}{3}$.

(a) Determine $M^{-1}$ in terms of $a$.

(3)

Given that $M^{-1} = 2M + 8I$ where $I$ is the $2 \times 2$ identity matrix,

(b) determine the value of $a$.

(3)