2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Determinants & Matrices

JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Determinats

  • question_answer
    If adj \[B=A,\] \[\left| P \right|=\left| Q \right|=1,\] then adj \[({{Q}^{-1}}B{{P}^{-1}})\]is

    A) \[PQ\]

    B) \[QAP\]

    C) \[PAQ\]

    D) \[P{{A}^{-1}}Q\]

    Correct Answer: C

    Solution :

    [c] Given \[adj\,B=A,\left| P \right|=\left| Q \right|=1\] Consider, adj \[({{Q}^{-1}}B\,{{P}^{-1}})\] \[=(adj\,{{P}^{-1}})(adj\,\,B)(adj\,\,{{Q}^{-1}})\] \[={{(adj\,P)}^{-1}}A.{{(adj\,Q)}^{-1}}={{({{P}^{-1}})}^{-1}}A{{({{Q}^{-1}})}^{-1}}\] \[=PAQ\].


You need to login to perform this action.
You will be redirected in 3 sec spinner