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Math Help - Matrices Question

  1. #1
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    Nov 2009
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    Matrices Question

    Hi, can someone please help me with this question:

    Let K be the finite field with only the two elements 0 and 1, where 1+1=0
    (i) How many 2x2 matrices with entries in K are there?
    (ii) How many of these are non singular?


    I understand that the question is refering to the field Z(integers) mod 2, but I'm not sure how that relates the matrices in question


    Thank you!!
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Quote Originally Posted by pseudonym View Post
    Hi, can someone please help me with this question:

    Let K be the finite field with only the two elements 0 and 1, where 1+1=0
    (i) How many 2x2 matrices with entries in K are there?
    (ii) How many of these are non singular?


    I understand that the question is refering to the field Z(integers) mod 2, but I'm not sure how that relates the matrices in question


    Thank you!!
    1. 2^4.
    2. (2^2 - 1)(2^2 - 2) = 6. See here.
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