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Math Help - Matrices which are their own inverses

  1. #1
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    Matrices which are their own inverses

    I need to find all 2x2 matrices A,
    (a b)
    (c d)
    such that A^2=I2, the 2x2 identity matrix.
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  2. #2
    tah
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    this means that A is equal to its inverse. So you may write the expression of A^{-1} and deduce 4 equations from the identification of it with A. It remains to solve these equations
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Snooks02 View Post
    I need to find all 2x2 matrices A,
    (a b)
    (c d)
    such that A^2=I2, the 2x2 identity matrix.
    Just to flesh out what tah said:

    you have \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}

    now, compute the matrix product on the left hand side, then equate corresponding components to get your 4 equations that tah spoke of. solve this system for your solution
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  4. #4
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    A=\begin{bmatrix} a&b \\ \frac{1-a^2}{b} &-a \end{bmatrix}\ or\ \pm I_2
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