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Math Help - Could you verify? F3-Field

  1. #1
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    Could you verify? F3-Field

    Hi,

    could you verify my solution? I want the determinant of the following and I got 0 wich I wouldn't expect. Dou you get this to?

    A \in M_{4}(\mathbb{F}_{3})

    A = \begin{pmatrix} 0 & 1 & 1 & 2 \\ 2 & 0 & 1 & 1 \\ 2 & 2 & 0 & 1 \\ 1 & 2 & 2 & 0 \end{pmatrix}

    det(A)=0 in my solution

    thanks
    greetings
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  2. #2
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    my calculator says ...

    \det(A) = -23
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  3. #3
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    Quote Originally Posted by skeeter View Post
    my calculator says ...

    \det(A) = -23
    If we are in \mathbb{Q} or \mathbb{R} yes, but the field is \mathbb{F}_{3} and -23 \notin \mathbb{F}_{3}

    But anyway thanks
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  4. #4
    Lord of certain Rings
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    Quote Originally Posted by Herbststurm View Post
    yes, but the field is \mathbb{F}_{3} and -23 \notin \mathbb{F}_{3}
    So what? Just read -23 modulo 3
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