Let {D1,D2,D3,........,Dn} be the set of all third order determinants that can be made with the distinct non-zero real number a1,a2,a3,........,a0 ,then,

the answer is - summation i=1 to n Di = 0 .How?

Please explain me briefly.

The number of third order determinants, = The number of arrangement of nine different numbers in nine places=9!Corresponding to each determinant made, there is a determinant obtained byinterchanging two consecutive rows or columns, So sum of this pairs will be 0.So the sum of all the determinants=0+0+0....9!2 times=0 

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