If =- 1 2 +i 3 2 then what is vmatrix 1+ &1+ ^2& + ^2 1& & ^2 1 & 1 ^2 &1 vmatrix equal to?

NDA 2024 Mathematics question

If then what is equal to?

Answer: (A)

is a complex cube root of unity, so and . First row: , ,

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Question ID VK-029903