If Δ = vmatrix a and b and c d and e and f g and h and i vmatrix...

The sum of the products of elements of any row or column with their corresponding cofactors is equal to the determinant $\Delta$.

Expanding the determinant along the first row, we get:
$aA + bB + cC = \Delta$

Expanding the determinant along the first column, we get:
$aA + dD + gG = \Delta$

Subtracting the second equation from the first equation, we get:
$(aA + bB + cC) - (aA + dD + gG) = \Delta - \Delta$

$bB + cC - dD - gG = 0$

Answer: $0$