Let’s start by describing before the first row element which lie in cutting the first row
with third column and before third row element which lie in cutting the third row
with third column ( 13 33 a and a ), as well in same manner let’s describe after first and
third row elements ( 11 31 a and a ), respectively. Now get such a scheme
This scheme will be formed of six diagonals with three different elements of
determinants. The elements products in three diagonals in left side will get the “+”
sign, in the other hand the elements products in three other different diagonals in right
side will get “-“sign. This will produce three terms with “+”sign and three other terms
with “-“sign, which in fact presents the definition formula to compute the
determinants of third order.