if$\omega \ne 1$ is a cube root of unity and $x+y+x\ne 0,$ then prove that $\left|\begin{array}{ccccc}\frac{x}{1+\omega }& & \frac{y}{\omega +{\omega }^2}& & \frac{z}{{\omega }^2+1}\\ \frac{y}{\omega +{\omega }^2}& & \frac{z}{{\omega }^2+1}& & \frac{x}{1+\omega }\\ \frac{z}{{\omega }^2+1}& & \frac{x}{1+\omega }& & \frac{y}{\omega +{\omega }^2}\end{array}\right|$

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