" 2."|[1+x,y,z],[x,1+y,z],[x,y,1+z]|=1+x+y+z

|[x,1,y+z],[y,1,z+x],[z,1,x+y]|=

Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0 .

Find the value of : |(1+x,y,z),(x,1+y,z),(x,y,1+z)|

For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z^2 ,1+p z^3]|=(1+p x y z)(x-y)(y-z)(z-x) .

The value of the det. |[x+y,y+z,z+x],[z,x,y],[1,1,1]| is

The value of |[[1,x,y+z],[1,y,z+x],[1,z,x+y]]| is

Find the value of x,y, and z if A=[[0,2y,z],[x,y,-z],[x,-y,z]] satisfies A^1=A^(-1) .

The value of |[x+y, y+z, z+x] , [z,x,y] , [1,1,1]| is

|(x,1,y+z),(y,1,z+x),(z,1,x+y)|=

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