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Determinants

Question
CBSEENMA12034690
Wired Faculty App

If A is an invertible matrix of order 2, then det (A–1) is equal to

  • det (A)

  • fraction numerator 1 over denominator det space left parenthesis straight A right parenthesis end fraction

  • 1

  • 0

Solution

B.

fraction numerator 1 over denominator det space left parenthesis straight A right parenthesis end fraction

We know that
               AA to the power of negative 1 end exponent space equals space straight I
  therefore space space space space space open vertical bar AA to the power of negative 1 end exponent close vertical bar space equals space space open vertical bar straight I close vertical bar space space space space space space space space space space space space space space rightwards double arrow space space space space space left parenthesis straight A right parenthesis space open vertical bar straight A to the power of negative 1 end exponent close vertical bar space equals space straight I therefore space space space space space open vertical bar straight A to the power of negative 1 end exponent close vertical bar space equals space fraction numerator 1 over denominator open vertical bar straight A close vertical bar end fraction therefore space space space space left parenthesis straight B right parenthesis space is space correct space answer.

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