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Math Help - A quick question in determinants

  1. #1
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    A quick question in determinants

    Let A be a real 101x101 matrix.
    If A is anti-symmetric, then |A^1001 + A^1003|= 0.

    Why is this true? This was the correct answer to a multiple-choice question.
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  2. #2
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    Re: A quick question in determinants

    note that 101 is odd.

    therefore, det(A) = det(-At) = (-1)101det(At) = -det(A) (since det(A) = det(At)),

    hence det(A) = 0.

    now A1001 + A1003 = (A1001)(I + A2),

    thus det(A1001 + A1003) = det(A1001)det(I + A2)

    = (det(A))1001(det(I + A2)) = (0)(det(I + A2)) = 0
    Last edited by Deveno; July 20th 2012 at 04:58 PM.
    Thanks from loui1410
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