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[Solved] Let A be a 3x3 matrix such that det (A)=-1 det (I_3-A)=3 where I_3 is the 3x3 identity matrix. Compute det

Question: Let A be a 3x3 matrix such that

  1. \(\det \left( A \right)=-1\)
  2. \(\det \left( {{I}_{3}}-A \right)=3\)

where \({{I}_{3}}\) is the 3x3 identity matrix. Compute \(\det \left( {{A}^{22}}-{{A}^{23}} \right)\).

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