If  then what is  equal to? 

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 0
  2. ω 
  3. ω2
  4. 1 - ω2

Answer (Detailed Solution Below)

Option 1 : 0
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NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

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Concept:

Determinant and Column Operations:

  • The determinant of a matrix is a scalar value representing area, volume, or invertibility.
  • Column operations like can simplify a determinant.
  • If one column (or row) becomes a linear combination of others or zero, the determinant becomes 0.
  • is a cube root of unity with identity: .

 

Calculation:

Let

⇒ Apply column operation:

⇒ First column becomes:

⇒ Using identity:

⇒ First column becomes:

⇒ New matrix:

⇒ Since first column is all zero,

∴ Determinant I = 0

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