`[[x,x^2, 1+x^2],[y, y^2, 1+y^2],[z, z^2, 1+z^2]]` where x,y,z are distinct. What is |A|.

If |(x,x^(2),1+x^(2)),(y,y^(2),1+y^(2)),(z,z^(2),1+z^(2))| where x, y, z are distinct what is |A| ?

Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove that x y z=-1 .

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|

If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):} , (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........