Why the determinant of a matrix with the sum of each row's elements equal 0 is 0? I'm trying to understand the proof of a problem, but I'm stuck. In my book they consider that if all lines of a matrix has sum 0 then it's determinant is also 0. I checked some random examples and it's true, but I couldn't proof it. Could you help me?

Another way to derive this result:
When the sum of all rows are zero, the row vectors are linearly dependent. Hence the determinant is zero. 
In fact, if any two or three or four rows add up to pure zero, the determinant is zero as well.
