I have got the matrix 

\begin{pmatrix} 0 & 0 & 0,4 \\ 0,75 & 0 & 0 \\ 0 & 0,8 & 0,8 \end{pmatrix} 

Now I need to get the inverse matrix but calculated in steps 
and not generated by the calculator. 

I know that the correct solution is:

\begin{pmatrix} 0 & 4/3 & 0 \\ -2,5 & 0 & 1,25 \\ 2,5 & 0 & 0 \end{pmatrix} 

My problem is that there are too many zeroes so 
I fail calculating the inverse matrix. 

The way I need to calculate the is to write the original matrix on the left side and the identity matrix on the right:

\begin{pmatrix} 0 & 0 & 0,4 & 1 & 0 & 0 \\ 0,75 & 0 & 0 & 0 & 1 & 0\\ 0 & 0,8 & 0,8 & 0 & 0 & 1\end{pmatrix} 

My Calculation steps:
 \begin{pmatrix} 0 & 0 & 0,4 & 1 & 0 & 0 \\ 0,75 & 0 & 0 & 0 & 1 & 0\\ 0 & 0,8 & 0,8 & 0 & 0 & 1\end{pmatrix}

subtraction of the second line and the first:

\begin{pmatrix} 0,75 & 0 & 0,4 & 1 & -1 & 0 \\ 0,75 & 0 & 0 & 0 & 1 & 0\\ 0 & 0,8 & 0,8 & 0 & 0 & 1\end{pmatrix}

subraction of the second line and the first, 
and subtraction of the third line and the first:

\begin{pmatrix} 0,75 & 0 & 0,4 & 1 & -1 & 0 \\ 0 & 0 & 0,4 & 1 & -2 & 0\\ 0 & -0,8 & -0,4 & 1 & -1 & -1\end{pmatrix}

subtraction of the third line and the first:

\begin{pmatrix} 0,75 & 0 & 0,4 & 1 & -1 & 0 \\ 0 & 0 & 0,4 & 1 & -2 & 0\\ 0 & 0,8 & 0,8 & 0 & 0 & 1\end{pmatrix}

while researching I figured out that I have to make at first the elements a21, a31 & a32 have to be set at first to null and then 
a12, a13 & a23. 

I do not know how to solve that.