For what values of x y and z ... The inverse fail to exist

[Idealistic]

Find the inverse of the matrix B(3x3):

...........1 x x[sup:3rkb7hef]2[/sup:3rkb7hef]
...........1 y y[sup:3rkb7hef]2[/sup:3rkb7hef]
...........1 z z[sup:3rkb7hef]2[/sup:3rkb7hef]

for what values of x,y, and z does the inverse of matrix B fail to exist?

I found the inverse via maple, and B[sup:3rkb7hef]-1[/sup:3rkb7hef] was just a 3x3:
Matrix(3, 3, {(1, 1) = y*z/(y*z-x*y+x^2-x*z), (1, 2) = -x*z/(-x*z+x*y+y*z-y^2), (1, 3) = x*y/(-x*z+x*y+z^2-y*z), (2, 1) = -(y+z)/(y*z-x*y+x^2-x*z), (2, 2) = (x+z)/(-x*z+x*y+y*z-y^2), (2, 3) = -(x+y)/(-x*z+x*y+z^2-y*z), (3, 1) = 1/(y*z-x*y+x^2-x*z), (3, 2) = -1/(-x*z+x*y+y*z-y^2), (3, 3) = 1/(-x*z+x*y+z^2-y*z)})

essentially it was either +(xy), +(xz), or +(yz) in the numerator and the denominator had a huge quadratic form of x,y's and z's.

I know one of the rows have to equal zero in the matrix in order for the inverse to fail to exist, but im having a hard time interpreting B[sup:3rkb7hef]-1[/sup:3rkb7hef]
.

 

[qpmathelp]

the inverse does not exist if the determinant =0


that is if (x-y)(y-z)(z-x) =0

or if x =y or y=z or z=x

http://rbmix.com/problem/math/determinant/determinant.html