If omega!=1 is a cube root of unity and ...

If `omega!=1` is a cube root of unity and `x+y+z!=0,` then prove that `|[x/(1+omega), y/(omega+omega^2),z/(omega^2+1)],[y/(omega+omega^2),z/(omega^2+1),x/(1+omega)],[(z)/(omega^2+1),x/(1+omega),y/(omega+omega^2)]|=0` if `x=y=z`

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if omega!=1 is cube root of unity and x+y+z != 0 then |[x/(1+omega),y/(omega+omega^2),z/(omega^2+1)],[y/(omega+omega^2),z/(omega^2+1),x/(1+omega)],[z/(omega^2+1),x/(1+omega),y/(omega+omega^2)]| =0 if

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