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Math Help - Determinants

  1. #1
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    Determinants

    Hi,
    Can you help me with this problem, please
    Suppose that A is nxn with n odd and that AT=-A. Show that
    (i)If 2≠0 in K then det(A)=0
    (ii) If 2=0 but we assume that each diagonal entry of A equals 0, then det(A)=0
    Thank you!
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  2. #2
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    Quote Originally Posted by mivanova View Post
    Hi,
    Can you help me with this problem, please
    Suppose that A is nxn with n odd and that AT=-A. Show that
    (i)If 2≠0 in K then det(A)=0
    (ii) If 2=0 but we assume that each diagonal entry of A equals 0, then det(A)=0
    Thank you!
    \det (A) = \det (A^T) =\det (-A) = (-1)^n \det (A) = -\det (A)
    Thus, 2\det (A) = 0.

    Now if \text{char}(K)\not = 2 then it must mean \det (A) = 0.
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