$\displaystyle M = \left[\begin{matrix}a&b&c\\d&e&f\\g&h&j\end{matrix}\righ t]$.
You know $\displaystyle M\mathbf{p} = \mathbf{q}, M\mathbf{q} = -2\mathbf{r}, M\mathbf{r} = 2\mathbf{p}+ 4\mathbf{q}$.
So perform these multiplications to give you a set of equations to solve for $\displaystyle a,b,c,d,e,f,g,h,j$.
On the contrary, i thought it would be easier and clearer if i attached it as a file.. i'll make sure to type it out next time.
If you are willing to help...I managed to find Matrix M as ( -1 3 1 )
0 4 2
1 -1 1
However for the second part M-1p i keep getting ( 1 ) .. which is wrong..
-5/8
0