I don't understand this :(adsbygoogle = window.adsbygoogle || []).push({});

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 ?

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# Odd determinant

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