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

Options

  1. A25
  2. B10
  3. C125
  4. D5

Correct answer

A. 25

Step-by-step solution

Given the property of the adjoint of a matrix, A( adj A) = |A|I . Comparing this with the given equation A( adj A) = 5I , we find that |A| = 5 . The determinant of the adjoint of a matrix of order n is given by | adj A| = |A|^ n-1 . Here, the order of the matrix n = 3 . Substituting the values, | adj A| = 5³⁻¹ = 5^2 = 25 . Answer: 25

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