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$\begingroup$ Slightly less general, AB a diagonal matrix and BA another diagonal matrix (and no negative coefficients, etc.) should give at most one element in each row and column of both A and B. Then invertibility gives exactly one and that they are permutation matrices comes from the coefficients being nonnegative integers. However, I am glad you wrote up the proof I was thinking. Gerhard "Ask Me About System Design" Paseman, 2011.04.19 $\endgroup$

Gerhard Paseman
– Gerhard Paseman

2011-04-19 20:42:09 +00:00
Commented Apr 19, 2011 at 20:42

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