# Answer to Question #18125 in Linear Algebra for Gibran

Question #18125

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.

Expert's answer

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.

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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