1. I have been teaching myself matrices for my IGCSE course and I ran into a problem in a past paper which I have no clue how to solve. The problem is part b of the attached image. Thanks for your help in advance.

2.

3. $[M]^{-1} \cdot [M] = [I]$

$\begin{bmatrix} -5t & 6\\ t & -t \end{bmatrix} \cdot \begin{bmatrix} t & 6\\ t & 5t \end{bmatrix}= \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}$

Multiply $[M]^{-1} \cdot [M]$ , then set each corresponding element in the product equal to the elements in the identity matrix to get the desired equation in $t$.

Give it a go and see how you do ...