Matrix: a special technique for finding the determinant of 3x3 matrix

Duplicate column method for 3x3 matrix:
For ONLY a 3x3 matrix write down the first two columns after the third column
|00 01 02|......|00 01 02| 00 01
|10 11 12| => |10 11 12| 10 11
|20 21 22| .....|20 21 22| 20 21

det = sum of the products of the diagonal elements from left to right - sum of the products of the diagonal elements from right to left

det = 00*11*22 + 01*12*20 + 02*10*21 - 02*11*20 - 00*12*21 - 01*10*22

PS: This technique works only for 3x3 matrices

I felt this method is simple and efficient for 3x3 for a bareis' fraction free algorithm. Please correct me if I am wrong.