Although not entirely relevant to this course, this is an interesting way to compute the determinant of a 3x3 matrix. Usually the second term would be -b(di-fg), so the pairings of elements are more intuitive (not overflowing the edge of the matrix). This is more easily seen with larger matrices when we must compute the determinant of a sub 3x3 matrix, where the overflowing pairings of elements are not as obvious (since they are not overflowing the entire matrix, only the sub 3x3 matrix). Either way, I assume there are better methods of computing determinants of large matrices by hand.
Although not entirely relevant to this course, this is an interesting way to compute the determinant of a 3x3 matrix. Usually the second term would be -b(di-fg), so the pairings of elements are more intuitive (not overflowing the edge of the matrix). This is more easily seen with larger matrices when we must compute the determinant of a sub 3x3 matrix, where the overflowing pairings of elements are not as obvious (since they are not overflowing the entire matrix, only the sub 3x3 matrix). Either way, I assume there are better methods of computing determinants of large matrices by hand.