Calculate the inverse of a complex matrix I am trying to calculate the inverse of a given matrix but somewhere I have an error in my calculation that I cannot find
$$\begin{array}{ccc}
&&
\left(
\begin{array}{ccc|ccc}
1-i & 2 & 1+i & 1 & 0 & 0 \\
0 & 1+3i & 1+4i & 0 & 1 & 0 \\
4+i&6+2i&2+i & 0 & 0 & 1
\end{array}
\right)
\begin{array}{cl}
| & \cdot\, (1+i)\\
&\\
|& \cdot\, (8-2i)
\end{array}\\
&\leadsto&
\left(
\begin{array}{ccc|ccc}
2 & 2+2i & 2i & 1+i & 0 & 0 \\
0 & 1+3i & 1+4i & 0 & 1 & 0 \\
34&52+4i&18+4i & 0 & 0 & 8-2i
\end{array}
\right)
\begin{array}{cl}
&\\
&\\
|&-17\cdot I
\end{array}
\\
&\leadsto&
\left(
\begin{array}{ccc|ccc}
2 & 2+2i & 2i & 1+i & 0 & 0 \\
0 & 1+3i & 1+4i & 0 & 1 & 0 \\
0&18-30i&18-30i & -17-17i & 0 & 8-2i
\end{array}
\right)
\begin{array}{cl}
&\\
|&\cdot\,(1-3i)\\
|&\cdot\,(18+30i)
\end{array}\\
&\leadsto&
\left(
\begin{array}{ccc|ccc}
2 & 2+2i & 2i & 1+i & 0 & 0 \\
0 & 4 & 13+i & 0 & 1-3i & 0 \\
0&1224&1224& 204-816i & 0 & 204+204i
\end{array}
\right)
\begin{array}{cl}
&\\
&\\
|& :\,102
\end{array}
\\
&\leadsto&
\left(
\begin{array}{ccc|ccc}
2 & 2+2i & 2i & 1+i & 0 & 0 \\
0 & 4 & 13+i & 0 & 1-3i & 0 \\
0&12&12 & 2-8i & 0 & 2+2i
\end{array}
\right)
\begin{array}{cl}
&\\
&\\
|&-3\cdot II
\end{array}\\
&\leadsto&
\left(
\begin{array}{ccc|ccc}
2 & 2+2i & 2i & 1+i & 0 & 0 \\
0 & 4 & 13+i & 0 & 1-3i & 0 \\
0&0&-27-3i & 2-8i & -3+9i & 2+2i
\end{array}
\right)
\end{array}
$$
Now i would "devide" by $\left(-27-3i\right)$ and then for example the second entry of the third line on the right sight should be $-i$ (see Wolfram Alpha) but obviously I get a different result.
Can you spot any error in my calculations?

Here is an error that I found. In the step where you multiply row two by $1-3i$, the second row should become $(0,\ 10,\ 13+i)$. You have it as $(0,\ 4,\ 13+i)$.
