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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2002

  • question_answer
    If \[A=\left[ \begin{matrix}    2 & -1  \\    -1 & 2  \\ \end{matrix} \right]\]and\[I\]is the unit matrix of order two, then\[{{A}^{2}}\]is equal to:

    A)  \[4A-3I\]        

    B)                         \[3A-4I\]

    C)                         \[A-I\]                                 

    D)                         \[A+I\]

    E)                         none of these

    Correct Answer: A

    Solution :

    \[{{A}^{2}}=\left[ \begin{matrix}    2 & -1  \\    -1 & 2  \\ \end{matrix} \right]\left[ \begin{matrix}    2 & -1  \\    -1 & 2  \\ \end{matrix} \right]\] \[=\left[ \begin{matrix}    4+1 & -2-2  \\    -2-2 & 1+4  \\ \end{matrix} \right]=\left[ \begin{matrix}    5 & -4  \\    -4 & 5  \\ \end{matrix} \right]\] \[=4A-3I\]          


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