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NDA2017MathematicsDeterminantsActual

If | array ccc x & y & 0 0 & x & y y & 0 & x array |=0 , then which one of the following is correct?

Options

  1. Ax y is one of the cube roots of unity
  2. Bx is one of the cube roots of unity
  3. Cy is one of the cube roots of unity
  4. Dx y is one of the cube roots of -1

Correct answer

D. x y is one of the cube roots of -1

Step-by-step solution

aligned & | array lll x & y & 0 0 & x & y y & 0 & x array |=0 x ( x ^2-0 )- y (0- y ^2 )+0=0 & x ^3+ y ^3=0 aligned aligned & x^3=-y^3 & x^3 y^3 =-1 ( x y )^3=-1 x y = [3] -1 aligned

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