Let
`|{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}| " and " Delta_(2)= |{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}| `.Then `Delta_(1)Delta_(2)` is equal to

Options

A. `Delta_(2)^(6)`
B. `Delta_(2)^(4)`
C. `Delta_(2)^(3)`
D. `Delta_(2)^(2)`

Answer

C

Explanation

the given determinant `Delta_(1)` is obtained by corresponding cofactors or determinant `Delta_(2)` and hence `Delta_(1)= Delta_(2)^(2)`
Now `Delta_(1)Delta_(2) =Delta_(2)^(2) Delta_(2) =Delta_(2)^(2)`