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If A( adj A)=5 I , where I is the identity matrix of order 3 , then | adj A| is equal to

Options

  1. A125
  2. B25
  3. C5
  4. D10

Correct answer

B. 25

Step-by-step solution

We have, array ll & A( adj A)=5 I & |A( adj A)|=|5 I| & |A|| adj A|=5³|I| [|K B|=K^ n |B| ] & |A||A|³⁻¹=125 I [| adj A|=|A|^ n-1 ] & |A|³=125 array |A|=5 Now, | adj A|=|A|^ n-1 =|A|² [n=3] =(5)²=25

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