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Math Help - groups

  1. #1
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    groups

    I need help on the following problem:
    Let a be the rotation about the origin in the plane and let p be the reflection in the x-axis. Show that pap-1=a-1.
    Thanks
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  2. #2
    ynj
    ynj is offline
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    Quote Originally Posted by thomas_donald View Post
    I need help on the following problem:
    Let a be the rotation about the origin in the plane and let p be the reflection in the x-axis. Show that pap-1=a-1.
    Thanks
    you may use matrix to explain it.
    the rotation can be represented as a=\left(\begin{array}{cc}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{array}\right  )
    the reflection can be represented as p=\left(\begin{array}{cc}1&0\\0&-1\end{array}\right)
    So pa=\left(\begin{array}{cc}\cos\theta&-\sin\theta\\-\sin\theta&-\cos\theta\end{array}\right)
    papa=(pa)^2=\left(\begin{array}{cc}1&0\\0&1\end{ar  ray}\right)=I
    Thus pap=a^{-1}\Rightarrow pap^{-1}=a^{-1}since p=p^{-1}
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  3. #3
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    Thank you very much for your help.
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