The numerical value of a determinant of the order 3 only can be determined by a sophisticated technique called, Sarrus expansion method. The algorithm of the method is briefed here as under:
(i) Place the given determinant as it is and then repeat its first two columns adjacent to its column 3.
(ii) Find the products of the elements along the leading diagonal and also those of the other two diagonals parallel to it. Get all the products summed up.
(iii) Find the products of the elements along the other 3 opposite diagonals and get them totaled.
(iv) Subtracted the total of the product under the item (iii) above from the total of the products under the item (ii) above, and get the difference thereof as the required value of the given determinant.
The above algorithm of the Sarrus expansion method can be clearly presented through the diagram called ‘Sarrus diagram’ as under: