IAL 2026 Jan A FP1 Q9

Question

[!problem]

$A = \begin{pmatrix} 6 & 4 \\ -1 & 1 \end{pmatrix}$

(a) Show that $A$ is non-singular.

(2)

The triangle $R$ is transformed to the triangle $S$ by the matrix $A$.

Given that the area of the triangle $R$ is 10 square units,

(b) find the area of triangle $S$.

(2)

Given that $B = A^4$ and that the triangle $R$ is transformed to the triangle $T$ by the matrix $B$,

(c) find, without evaluating $B$, the area of triangle $T$.

(2)