Correct Answer - B::C
In the left - hand determinant each element is the cofactor of the elements of the determinant
`|{:(x,,y,,z),(y,,z,,x),(z,,x,,y):}|=Delta " (says) "`
hence
`Delta^(2) = |{:(x,,y,,z),(y,,z,,x),(z,,x,,y):}||{:(x,,y,,z),(y,,z,,x),(z,,x,,y):}|`
`=|{:(x^(2)+y^(2)+z^(2),,xy+yz+zx,,xz+yx+zy),(Sigmaxy,,Sigmax^(2),,Sigmaxy),(Sigmaxy,,Sigmaxy,,Sigmax^(2)):}|`
`|{:(r^(2),,u^(2),,u^(2)),(u^(2),,r^(2),,u^(2)),(u^(2),,u^(2),,r^(2)):}|" "underset(xy+yz+zx=u^(2))("Where "x^(2)+y^(2)+z^(2)=r^(2))`