Solution:
Given
It is also given that \[\omega \] is a complex cube root of unity,
Consider the LHS,
We know that \[1\text{ }+\text{ }\omega \text{ }+\text{ }{{\omega }^{2}}~=\text{ }0\text{ }and\text{ }{{\omega }^{3}}~=\text{ }1\]
Now by simplifying we get,
Again by substituting \[1\text{ }+\text{ }\omega \text{ }+\text{ }{{\omega }^{2}}~=\text{ }0\text{ }and\text{ }{{\omega }^{3}}~=\text{ }1\] in above matrix we get,
Therefore \[LHS\text{ }=\text{ }RHS\]
Hence the proof.