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Question

If omega blank open parentheses not equal to 1 close parentheses is a cube root of unity, then value of the determinantopen vertical bar table row 1 cell 1 plus i plus omega to the power of 2 end exponent end cell cell omega to the power of 2 end exponent end cell row cell 1 minus i end cell cell negative 1 end cell cell omega to the power of 2 end exponent minus 1 end cell row cell negative i end cell cell negative i plus omega minus 1 end cell cell negative 1 end cell end table close vertical bar is

  1. 0    
  2. 1    
  3. i    
  4. omega    

The correct answer is: 1


    open vertical bar table row 0 cell 1 plus omega plus omega to the power of 2 end exponent end cell 0 row cell 1 minus i end cell cell negative 1 end cell cell omega to the power of 2 end exponent minus 1 end cell row cell negative i end cell cell negative 1 plus omega minus 1 end cell cell negative 1 end cell end table close vertical bar
    equals open vertical bar table row 0 0 0 row cell 1 minus i end cell cell negative 1 end cell cell omega to the power of 2 end exponent minus 1 end cell row cell negative 1 end cell cell negative i plus omega minus 1 end cell cell negative 1 end cell end table close vertical bar blank left square bracket because 1 plus omega plus omega to the power of 2 end exponent equals 0 right square bracket
    (Operating R subscript 1 end subscript rightwards arrow R subscript 1 end subscript minus R subscript 2 end subscript plus R subscript 3 end subscript)

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