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  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    If AB = A, BA = B for any two square matrices A and B, then\[{{A}^{2}}\]is equal to

    A)  A               

    B)  B

    C)  AB              

    D)  \[{{B}^{2}}\]

    Correct Answer: D

    Solution :

     Given, \[AB=A\Rightarrow B=\text{ }I\] and \[BA=B\Rightarrow A=I\] Now,       \[{{A}^{2}}=A.A\] \[=AB.A\] \[=A.BA\] \[=I.B\] \[=B.B={{B}^{2}}\]


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