सिद्ध कीजिए कि
`|(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)|`.

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zy,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(y-z)(z-x)(x-y)(yz+zy+xy)

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]|

" (d) "|[x,y,z],[x^(2),y^(2),z^(3)],[yz,zx,xy]|=|[1,1,1],[x^(3),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|

|[1/x,1/y,1/z],[x^(2),y^(2),z^(2)],[yz,zx,xy]|

(x-y-z)^(2)-(x^(2)+y^(2)+z^(2))=2(yz-zx-xy)

Show that, |[1,x,yz],[1,y,zx],[1,z,xy]|=|[1,x,x^(2)],[1,y,y^(2)],[1,z,z^(2)]|

Simplify- (x-y-z)(x^2+y^2+z^2+xy-yz+zx)

|[yz,x,x^(2)],[zx,y,y^(2)],[xy,z,z^(2)]|=|[1,x^(2),x^(3)],[1,y^(2),y^(3)],[1,z^(2),z^(3)]|