If A is an 7 x 7 matrix with all 49 entries being odd numbers. Show that det (A) is a multiple of 64. You may use the fact (without proving) that an n x n matrix with integer entries has an integer determinant.
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Expert's answer
2012-11-13T10:32:23-0500
First we subtract first rowfrom other rows. Thus we obtain six rows with all even entries. If we divide each of these rows by 2 then we have to multiply det(A) by 2^6=64.
Now det(A)=64*det(B), where all entries of B are again integer, so det(B) is integer too. And then detA is integer and multiply of 64.
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