Using properties of determinants, prove that `[[-yz, y^2+yz, z^2+yz], [x^2+xz, -xz, z^2+xy], [x^2+xy, y^2+xy, -xy]] = (xy+yz+zx)^2`

Using properties of determinants, prove that |{:(y^2z^2,yz,y+z),(z^2x^2,zx,z+x),(x^2y^2,xy,x+y):}|=0

By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)

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 the properties of determinants, show that : |[[x^2, y^2, z^2],[yz, zx, xy],[x,y,z]]|= (x-y)(y-z)(z-x)(xy+yz+zx) .

Using the properties of determinants, show that: [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

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

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

By using properties of determinants , show that : {:[( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) ]:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

By using properties of determinants , show that : {:[( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) ]:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

By using properties of determinants , show that : {:|( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) |:} =( x-y)(y-z) (z-x) (xy+yz+ zx)