First slide
Introduction to Determinants
Question

Let {D1, D2, D3, ..., Dn} be the set of third-order determinants that can be made with the distinct non-zero real numbers a1, a2, ..., a9. Then 

Moderate
Solution

The total number of third-order determinants is 9!. The number of determinants is even and of these there are 9!/2 pairs of determinants which are obtained by changing two consecutive rows, so i=1nDi=0.

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