You made a very simple mistake.
You have .
I still don't understand, isn't there the property:
If B is the matrix that results when a single row or column of A is multiplied by a scalar k, then
If I were to multiply det(A) by k=1/2 then I would get det(B)
Or is it that I'm just thinking of this all backwards?
I know for sure that if (from another example) if I divided a row by some scalar k, say I divided by 2, I would have something like so then