2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced AIEEE Solved Paper-2012

  • question_answer
    Let P and Q be \[3\times 3\] matrices \[P\ne Q\]. If \[{{P}^{3}}={{Q}^{3}}\] and \[{{P}^{2}}={{Q}^{2}}\], then determinant of \[({{P}^{2}}={{Q}^{2}})\] is equal to :   AIEEE  Solved  Paper-2012

    A) \[-2\]                                       

    B) 1

    C) 0                                                

    D) \[-1\]

    Correct Answer: C

    Solution :

                 Subtracting \[{{P}^{3}}-{{P}^{2}}Q={{Q}^{3}}-{{Q}^{2}}P\] \[{{P}^{2}}(P-Q)+{{Q}^{2}}(P-Q)=0\] \[({{P}^{2}}+{{Q}^{2}})(P-Q)=0\] If \[\left| {{P}^{2}}+{{Q}^{2}} \right|\ne 0\] then \[{{P}^{2}}+{{Q}^{2}}\] is invertible \[\Rightarrow P-Q=0\] contradiction Hence \[\left| {{P}^{2}}+{{Q}^{2}} \right|=0\]


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