Not technically a computer question, and not a plea for understanding.

I'm just a bit curious, and I hope maybe someone may have an answer, though I realize this isn't a math forum. I guess I'm just letting off a little math-related steam.

When doing the determinant of a 3x3 matrix, one way to calculate it is by doing a determinant by minors (see attached image).

Why is it that the standard notation has the second term with the determinant of [[d f][g i]]subtractedwhen it would be more logical toaddthe determinant of [[f d][i g]]? That nets the same answer and also creates a more logical pattern in the terms of the equation. If you get what I mean, it's like "shifting" the sub-matrix over, and the columns wrap around. It's been bugging me profusely that this isn't the case anywhere I look.

Edit: changed picture