Determinant of a matrix Having some problems with a determinant of a 4x4 matrix M.
$
M =
\left( {\begin{array}{cc}
1 & 2 & 3 &-1 \\
0 & 1 & 2 & 2 \\
1 &1 &0 &0 \\
3&1&2&0
\end{array} } \right)
$
Went along and developed it according to the 4th column. So I end up with two matrixes A and B.
$
A = -1 \cdot det 
\left( {\begin{array}{cc}
0 & 1 & 2 \\
1 & 1 & 0  \\
3 &1 &2  \\
\end{array} } \right)
$
$
B = 2 \cdot det
\left( {\begin{array}{cc}
1 & 2 & 3 \\
1 & 1 & 0  \\
3 &1 &2  \\
\end{array} } \right)
$
I get $A= (-1) \cdot((0 \cdot1\cdot2)+(1\cdot0\cdot3)+(2\cdot1\cdot1)-(3\cdot1\cdot2)-(1\cdot2\cdot2)-(1\cdot1\cdot0)) \\$
$A=(-1) \cdot(-6)=6$
$B= 2 \cdot((1\cdot1\cdot2)+(2\cdot0\cdot3)+(3\cdot1\cdot1)-(3\cdot1\cdot3)-(1\cdot2\cdot2)-(1\cdot1\cdot0))
\\$
$B = 2\cdot8=16$
$A+B=22$ 
which is wrong. Where is my mistake?
The correct answer should be $-22$ but I don't get why my solution keeps being positive.
Edit: im such a moron: A = 1* det and B = -2 * det. Everythings clearing up while in bed. Hehe!

 Your mistake was that you forgot the $(-1)^{i+j}$ for the cofactors.
