[SOLVED] Finding inverse matrix

Hi,I am trying to find the inverse of following matrix,

[0 1 0 0

-1 0 1 0

0 -1 0 1

0 0 -1 0]

I got every cofactor correctly except for one, a34,

Below is the procedure of trying to find the cofactor of a34, please tell me where I made the mistake,

[ 0 1 0

-1 x (-1)^(3+4)* -1 0 0

0 -1 1]

This becomes,

[ 0 1 0

-1 0 0

0 -1 1]

Now try to find the determinant using the first row, second column,

-1^(2+1) [ -1 0

0 1]

The answer i got is 1.

However, using the calculator the correct answer is -1.