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Math Help - Let A in M(nxn) (F). Under what conditions is det(-A)=det(A)

  1. #1
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    Post Let A in M(nxn) (F). Under what conditions is det(-A)=det(A)

    Hi All,
    Have a quick question

    Let A in M(nxn) (F). Under what conditions is det(-A)=det(A)

    Thanks
    sofwhere
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  2. #2
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    Quote Originally Posted by sofwhere View Post
    Hi All,
    Have a quick question

    Let A in M(nxn) (F). Under what conditions is det(-A)=det(A)

    Thanks
    sofwhere
    since \det(-A)=(-1)^n \det A, we have \det(-A)=\det A if and only if at least one of theses conditions holds:

    1) \det A = 0,

    2) 2 \mid n,

    3) \text{char}(F)=2.
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  3. #3
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    Quote Originally Posted by NonCommAlg View Post
    since \det(-A)=(-1)^n \det A, we have \det(-A)=\det A if and only if at least one of theses conditions holds:

    1) \det A = 0,

    2) 2 \mid n,

    3) \text{char}(F)=2.

    I thought of conditions 1 & 2. But the 3rd one is which i didnt think of. Thanks for timely reply.
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