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COMEDK202510 May 2025Evening ShiftMathematicsMatricesActual

If A( adj A)= [ array lll 5 & 0 & 0 0 & 5 & 0 0 & 0 & 5 array ] , then the value of |A|+| adj A| is equal to

Options

  1. A25
  2. B5
  3. C125
  4. D30

Correct answer

D. 30

Step-by-step solution

Given A( adj A) = 5I , where I is the identity matrix of order 3 3 . Using the property A( adj A) = |A|I , we compare the given matrix with |A|I . |A|I = bmatrix 5 & 0 & 0 0 & 5 & 0 0 & 0 & 5 bmatrix = 5I . Thus, |A| = 5 . Using the property | adj A| = |A|^ n-1 , where n is the order of the matrix A . Here n = 3 , so | adj A| = |A|³⁻¹ = |A|^2 . | adj A| = 5^2 = 25 . The value of |A| + | adj A| = 5 + 25 = 30 . Answer: 30

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