Factoring a constant from each row of matrix

[Derill03]

Why is it that a 16 comes out when you factor a 2 from each row of this matrix:

0 2 2 2
2 0 2 2
2 2 0 2
2 2 2 0

 

[dx]

Because 2*2*2*2 is 16 (one for each row). Determinants are linear in both columns and rows, so if you divide a column by 2, the determinant also becomes half as much as it was before. If you want to keep the value of the determinant the same, you have to multiply it by 2. So when you divide the first row by 2 to make it (0, 1, 1, 1), you have to multiply the whole thing by 2.