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If A is a matrix of order 4 such that A( adj A)=10 I , then | adj A| is equal to

Options

  1. A10
  2. B100
  3. C1000
  4. D10000

Correct answer

C. 1000

Step-by-step solution

Given, A( adj A)=10 I We know that A( adj A)=|A| I array ll & 10 I=|A| I & |A|=10 array We know that | adj A|=|A|^ n-1 , where n is order of A | adj A|=|A|⁴⁻¹=10^3=1000

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