MHB Solving a Matrix Problem on IGCSE Past Paper: Part B

[Funfinder15]

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.View attachment 9518

 

[skeeter]

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

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

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 ...