" (i) "|[y+z,x,x],[y,z+x,y],[z,z,x+y]|=4xyz

Show that abs([y+z ,x,x],[y,z+x,y],[z,z,x+y])=4xyz

Using properties of determinant show that : |(y+z,x,x),(y,z+x,y),(z,z,x+y)|=4xyz

|[y+z, x, x] , [y, z+x, y] , [z, z, x+y]|= (i) x^2y^2z^2 (ii) 4x^2y^2z^2 (iii) xyz (iv) 4xyz

Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz

Prove that |[y+z,z,y],[z,z+x,x],[y,x,x+y]]=4xyz

Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)