If detA 6= 0, at least one of the n! terms in the big formula (6) is not zero. Deduce

Chapter 4, Problem 4.3.21

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If detA 6= 0, at least one of the n! terms in the big formula (6) is not zero. Deduce that some ordering of the rows of A leaves no zeros on the diagonal. (Dont use P from elimination; that PA can have zeros on the diagonal.)

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