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Math Help - Invertible matrices problem

  1. #1
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    Invertible matrices problem

    Show that the square matrix 2N - I is its own inverse if N^{2} = N


    I really don't know where to start here. All I know is that I have to show that 2N - I = (2N - I)^{-1}.

    Any help is appreciated.
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  2. #2
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    Quote Originally Posted by temaire View Post
    Show that the square matrix 2N - I is its own inverse if N^{2} = N


    I really don't know where to start here. All I know is that I have to show that 2N - I = (2N - I)^{-1}.

    Any help is appreciated.
    What is (2N-I)(2N-I) ?
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  3. #3
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    Quote Originally Posted by Defunkt View Post
    What is (2N-I)(2N-I) ?
    That would be the identity matrix I right?
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  4. #4
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    Quote Originally Posted by temaire View Post
    That would be the identity matrix I right?
    This is what you need to show.

    What do you get when you expand (2N-I)(2N-I) ?
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  5. #5
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    Ok I think I got it.

    If I expand it, I will get the identity matrix.

    Thanks for the help.
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