ISRO Electrical Engineering (EE) 2023 - Question 27

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If A is a square matrix such that A(Adj A) = [[5, 0, 0], [0, 5, 0], [0, 0, 5]] then det (Adj A) =

  • A. 5
  • B. 25
  • C. 125
  • D. 625

Answer: B. 25

Explanation: A·adj(A) = |A|·I = 5·I, so |A| = 5. For a 3×3 matrix, det(adj A) = |A|^(n-1) = 5^(3-1) = 25.

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