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AP EAMCET2015MathematicsMatrices

If A is a square matrix of order 3, then | adj ( adj A^2 ) | is equal to

Options

  1. A|A|^2
  2. B|A|^4
  3. C|A|^8
  4. D|A|¹⁶

Correct answer

C. |A|^8

Step-by-step solution

Given matrix A is of order 3 . We know that, | adj ( adj A)|=|A|^ (n-1)^2 Similarly, | adj ( adj A^2 ) |= |A^2 |^ (3-1)^2 aligned & = |A^2 |^ 2^2 [ n=3] & = |A^2 |^4=|A|^8 aligned

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