Determinants in linear algebra

[Square1]

Homework Statement

i can't for the life of me find out where the negative comes from!

if you have the following the following determinant to calculate

det
(0) (1) (3) (4)
(2) (3) (1) (1)
(4) (-1) (-1) (2)
(6) (4) (-1) (1)and the next step shows... it equals (note negative sign)= -det
(2) (3) (1) (1)
(0) (1) (3) (4)
(4) (-1) (-1) (2)
(6) (4) (-1) (1)
how did they get the negative! which rule is this! The answer is -32 which. If i do it my way without adding the negative in at the first step, i get 32 so the rest of the steps i do are right.

Thanks!

 

[LCKurtz]

It's a general property of determinants that if you swap two rows or cols, it changes the sign of the determinant.

 

[Square1]

OMG ROWS TOO?? god it doesn't tell us that in our notes! only columns! thank you!