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Math Help - Invertible Matrix

  1. #1
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    Invertible Matrix

    I need to find the relationship between the number of 2 x 2 matrices and the number of invertible 2 x 2 matrices over Zp where p is a prime number.

    To help me, I took Z2 because 2 is a prime number. There appear to be 2^4=16 different matrices over Z2. Is this right?

    Of these, I found 6 of them to be invertible.

    Therefore, I think that the number of matrices is p^4. But I don't know the relationship between p and the number of invertible matrices. What is this?

    Thank you.
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  2. #2
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    Quote Originally Posted by thesummerofgeorge View Post
    I need to find the relationship between the number of 2 x 2 matrices and the number of invertible 2 x 2 matrices over Zp where p is a prime number.

    To help me, I took Z2 because 2 is a prime number. There appear to be 2^4=16 different matrices over Z2. Is this right?

    Of these, I found 6 of them to be invertible.

    Therefore, I think that the number of matrices is p^4. But I don't know the relationship between p and the number of invertible matrices. What is this?

    Thank you.
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