Prove `|[xy, xz, x^2+1] , [y^2+1, yz, xy] , [yz, z^2+1, xz]|= 1+x^2+y^2+z^2`

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]|

x ^(2) - xz + xy - yz =?

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

Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y^2+1,yz),(xz,yz,z^2+1)|=1+x^2+y^2+z^2

Using properties of determinants , prove that |(x^2+1,xy,zx),(xy,y^2+1,yz),(zx,yz,z^2+1)|=1+x^2+y^2+z^2

What is the LCM of (x^2 - y^2 – z^2 – 2yz),(x^2 - y^2 + z^2 + 2xz) and (x^2 + y^2 - z^2 - 2xy) ?

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):}|=(x-y) (y-z) (z-x) (xy+yz+zx)

Using properties of determinant show that : |(-x^2,xy,xz),(xy,-y^2,yz),(xz,yz,-z^2)|=4x^2y^2z^2