Linear Algebra 14TBD: Interesting 2x2 Determinant Examples

[tangolasher]

So you get ab - bc = 0 from a/b = c/d right?

I noticed that taking the equivalent -ab + bc = 0 OR ab - bc = 0, will yield a different determinant,
+2 instead of -2 in the case of the first matrix. This is still expressing the same relationship
between the columns of the matrix, and yet the sign totally changed. Doesn't seem okay to me...

Is there a reason why you must do the determinant subtraction in that particular order, and does the sign matter?