Finding a two-by-two matrix such that...

I need to find a matrix which would solve for the following: $$\begin{bmatrix}4 & 7\\4 & 2 \end{bmatrix} * \begin{bmatrix}- & -\\- &- \end{bmatrix} = \begin{bmatrix}1 & 0\\0 & 1 \end{bmatrix}$$

I tried using the inverse which gave me $ \begin{bmatrix}\frac{2}{-20} & \frac{-7}{-20}\\\frac{-4}{-20} & \frac{4}{-20} \end{bmatrix} $

Also attempted making $\Bigg [\begin{matrix}4 & 7\\4 & 2 \end{matrix}\Bigg | \begin{matrix}1 & 0\\0 & 1 \end{matrix}\Bigg ]$

which gave me the following: $\Bigg [\begin{matrix}1 & 0\\0 & 1 \end{matrix}\Bigg | \begin{matrix}\frac17 & 0\\\frac1{20} & \frac1{-5} \end{matrix}\Bigg ]$

I am guessing I did something wrong at some step but Cannot seem to figure out where!

via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/294447/finding-a-two-by-two-matrix-such-that