Problem of the month (matrices, determinants):
Let A be an n-by-n
matrix with integer entries such that each column
is a permutation of the first column of A.
Prove that the sum of the entries of this column
divides the determinant of A. For instance,
if A is the matrix
6 5 9
5 9 5
9 6 6
then, one checks that det(A) = -240 which
is divisible by 6 + 5 + 9 = 20.
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