If is a complex cube root of unity, then value of vmatrix x+1& & ^2 &x+ ^2&1 ^2&1&x+ vmatrix is

JEE Main Mathematics question

If is a complex cube root of unity, then value of is

Answer: (A)

The determinant is with ; the second and third rows of are and times the first row, so has rank . Its trace is

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Question ID VK-013642