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If A( adj A)= [ array ccc -2 & 0 & 0 0 & -2 & 0 0 & 0 & -2 array ] , then | adj A| equals

Options

  1. A-2
  2. B-4
  3. C4
  4. D8

Correct answer

C. 4

Step-by-step solution

Given A( adj A) = bmatrix -2 & 0 & 0 0 & -2 & 0 0 & 0 & -2 bmatrix = -2I , where I is the 3 3 identity matrix. Using the property A( adj A) = |A|I , we have |A| = -2 . The determinant of the adjoint of a matrix A of order n is given by | adj A| = |A|^ n-1 . Here, n = 3 and |A| = -2 . Therefore, | adj A| = (-2)³⁻¹ = (-2)^2 = 4 . Answer: 4

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