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AP EAMCET2007MathematicsMatrices

If A is a square matrix such that A( adj A)= [ array lll 4 & 0 & 0 0 & 4 & 0 0 & 0 & 4 array ] , then det ( adj A) is equal to

Options

  1. A4
  2. B16
  3. C64
  4. D256

Correct answer

B. 16

Step-by-step solution

aligned & Given A( adj A)= [ array lll 4 & 0 & 0 0 & 4 & 0 0 & 0 & 4 array ] & Now, |A( adj A)|= | array lll 4 & 0 & 0 0 & 4 & 0 0 & 0 & 4 array | & |A|| adj A|=4^3 & | adj A|=|A|^ n-1 & Here, n=3 & | adj A|=|A|^2 & . |A| A A |^2=64 & |A|^3=(4)^3 & |A|=4 & aligned aligned & Now, | adj A|=|A|^2=(4)^2 & | adj A|=16 & aligned

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