Let $\left\{\Delta_1,\Delta_2,.....,\Delta_n\right\}$ be the set of all determinants of order 3 that can be made with the distinct real numbers from the set $S=\left\{1,2,3,4,5,6,7,,8,9\right\}$.Then prove that $\sum_{i=1}^{n}\Delta_i=0$
I know that the total number of determinants that can be formed by using distinct real numbers from the given set is $9!$.But i dont know how to prove that their sum is zero.Please help me.Thanks