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If A is a matrix of order 4 such that A( adj A)=10 ~I , then | adj A| is equal to

Options

  1. A10000
  2. B1000
  3. C10
  4. D100

Correct answer

B. 1000

Step-by-step solution

Given that A is a square matrix of order n = 4 . The property of the adjoint of a matrix states that A( adj A) = |A| I . Comparing this with the given equation A( adj A) = 10 I , we find that |A| = 10 . The determinant of the adjoint of a matrix is given by the formula | adj A| = |A|^ n-1 . Substituting the values n = 4 and |A| = 10 , we get | adj A| = 10⁴⁻¹ = 10^3 . | adj A| = 1000 . Answer: 1000

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