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COMEDK2015MathematicsDeterminants

If A= [ array lll a & 0 & 0 0 & a & 0 0 & 0 & a array ] , then det ( adj A) is

Options

  1. Aa²⁷
  2. Ba⁹
  3. Ca⁶
  4. Da²

Correct answer

C. a⁶

Step-by-step solution

Since, A = [ array lll a & 0 & 0 0 & a & 0 0 & 0 & a array ] |A|=a a a=a³ Using formula | adj A|=|A|^ n-1 , we get det ( adj A)= (a³ )³⁻¹= (a³ )²=a⁶

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