I'm having trouble with this question.

Here is what I have:

From the hint, we solve the equation $\displaystyle \vec{y}=A(B\vec{x})$ first for $\displaystyle B(\vec{x})$ and then for $\displaystyle \vec{x}$. So we have

$\displaystyle B\vec{x}=A^{-1}\vec{y}$

so...

$\displaystyle \vec{x}=B^{-1}A^{-1}\vec{y}$

I'm really not sure where to go from here though.