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Odd determinant

  1. Sep 20, 2008 #1
    I don't understand this :

    let A is n x n matrix whose entries are precisely the numbers 1, 2, . . . , n^2.
    Put odd numbers into the diagonal of A, only even numbers above the diagonal and arrange the entries under the diagonal arbitrarily. Then det(A) is odd.

    What is the explanation ?
     
  2. jcsd
  3. Sep 20, 2008 #2

    HallsofIvy

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    What have you tried? In particular, have you tried seeing what happens for n= 2 and 3?
     
  4. Sep 22, 2008 #3
    for n=2 we have det(A) = -5. so what ?
     
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