GT1 is done backwards?

[StevenClontz]

We currently ask: if det(A) is known and we apply a row operation, what's the new determinant?

Would it make more sense to ask for det(A) given that A is the result of a row operation applied to a matrix with known determinant? This better models how to find determinants with row operations: I want to find det(A), so I apply row operations until eventually I get a matrix of known determinant.

[StevenClontz]

In particular, the equation is now det(C)=det(R)det(A), so we divide to get det(A)=det(C)/det(R). Which is why we divide by 2 ('factor out a 1/2") when we double a row, and multiply by 2 ("factor out a 2") when we halve a row.