System of equation, condition of a

For which values of $\displaystyle a$ the following system of equations has a unique solution? Infinite solutions?

$\displaystyle \left[ \begin{array}{ccc}x-y+z=2 \\ ax-y+z=2 \\ 2x-2y +(2-a)z=4a \end{array} \right]$.

I've solve the system via matrices and got that $\displaystyle \left[ \begin{array}{ccc}x=0 \\ y=-2-4a \\ z=-4a(a-1) \end{array} \right]$. I'm stuck from here... I see that for a given $\displaystyle a$ there is always a unique solution, but that you can give whatever value for $\displaystyle a$ so that you have an infinity of solutions. So how do I answer the question?