What is the value of the determinant `|{:(1," "1," "1),(1,1+xyz," "1),(" "1," "1,1+xyz):}|`?

|{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xy+yz+zx+xyz

The least value of the product xyz for which the determinant |(x,1,1),(1,y,1),(1,1,z)| is non-negative is

The least value of the product xyz for which the determinant |(x,1,1),(1,y,1),(1,1,z)| is non-negative, is: (A) -16sqrt2 (B) -2sqrt2 (C) -1 (D) -8

Given that xyz = -1 , the value of the determinant |(x,x^(2),1 +x^(3)),(y,y^(2),1 + y^(3)),(z,z^(2),1 +z^(3))| is

|(1+x,1,1),(1,1+y,1),(1,1,1+z)|=xy+yz+zx+xyz

Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1, 1+3z,1)| =9(3xyz+xy+yz+zx)

Using prperties of determinants, prove that : |(1,1,1+3x),(1+3y,1,1),(1,1+3z,1)| = 9(3xyz + xy + yz + zx) .

Using properties of determinants prove that ((1,1,1+3x),(1+3y,1,1),(1,1+3z,1)=9(3xyz+xy+yz+zx)

Show that : |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xyz(1+(1)/(x)+(1)/(y)+(1)/(z))

If x+y+z=xyz, then what is the value of tan^(-1)x+tan^(-1)y+tan^(-1)z ?