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COMEDK2012MathematicsComplex Number

If is a cube root of unity, then the value of determinant | array ccc 1+ & ² & ²+ & - & ² 1+ ² & & ² array | is equal to

Options

  1. A1+
  2. B1-
  3. C0
  4. D²

Correct answer

B. 1-

Step-by-step solution

We have, | array ccc 1+ & ² & ²+ & - & ² 1+ ² & & ² array | = | array ccc 1+ + ² & ² & ² & - & ² 1+ + ² & & ² array | (C₁ C₁+C₂ ) aligned &= | array ccc 0 & ² & ² & - & ² 0 & & ² array | & .=0- ² ( ⁴-0 )+ ( )³-0 ) &=- ⁶+ ⁴ aligned =-1+ [ ³=1 ]= -1

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