If `1.omega, omega^2` are the roots of unity, then `Delta=|(1,omega^n,omega^(2n)),(omega^(2n),1,omega^(n)),(omega^(n),omega^(2n),1)|`is equal to

Explanation

Given,`Delta=|(1,omega^n,omega^(2n)),(omega^(2n),1,omega^(n)),(omega^(n),omega^(2n),1)|`

`1+ω^n+ω^(2n)=0`

Now solving the given determinent, we have

`Delta=|(1,omega^n,omega^(2n)),(omega^(2n),1,omega^(n)),(omega^(n),omega^(2n),1)|`


Applying `C_1​→C_1​+C_2​+C_3​`

`Delta=|(1+omega^n+omega^(2n),omega^n,omega^(2n)),(1+omega^n+omega^(2n),1,omega^(n)),(1+omega^n+omega^(2n),omega^(2n),1)|`

`Delta=|(0,omega^n,omega^(2n)),(0,1,omega^(n)),(0,omega^(2n),1)|`

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