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JCECE Engineering JCECE Engineering Solved Paper-2012

  • question_answer
    A skew-symmetric matrix \[M\] satisfies the relation\[M+I=0\], where \[I\] is the unit matrix. Then, \[MM'\]is equal to

    A) \[I\]                                      

    B) \[2I\]

    C) \[-I\]                                     

    D)  None of these

    Correct Answer: A

    Solution :

    Since, \[M\] is skew-symmetric matrix \[M'=-M\] Also,      \[{{M}^{2}}+I=0\] \[\Rightarrow \]               \[{{M}^{2}}=-I+0=-I\] \[\Rightarrow \]               \[M\cdot M=-I\] \[\Rightarrow \]               \[M\,\,M\,\,M'=IM'=I(-M')=IM=M\] \[\Rightarrow \]               \[{{M}^{-1}}MMM'={{M}^{-1}}M\] \[\Rightarrow \]               \[IMM'=I\] \[\Rightarrow \]               \[MM'=I\]


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