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If ω is a cube root of unity, then find the value of the determinant  is

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  1. 3ω 
  2. -3ω
  3. 3ω2
  4. -3ω2

Answer (Detailed Solution Below)

Option 4 : -3ω2
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Detailed Solution

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Concept:

ω is a cube root of unity.

Property of cube root of unity:

  • ω3 = 1
  • 1 + ω + ω2  = 0

Calculations:

Given, ω is a cube root of unity.

⇒ω3 = 1, ad 1 + ω + ω2  = 0

Now, consider the determinant

 

Taking ω and -ω common from C2 and C3 respectively,

= 

=  

= 

= 

= 

= 0 - 3ω2

= - 3ω2

Hence the required value is -3ω2

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