n*n board if sum negative multiply every single number on (-1)

elene

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May 7, 2018
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Hello! I have not been able to solve this task and was wondering if somebody could help me solve it.

There is a board n*n, on which real numbers are written, operations are the following:

If the sum of numbers in a column or row is negative, then I have to multiply every single one of the numbers in this column or row on (-1).

I have to prove that it is not possible to carry out infinite number of this operations on the given board.

English is not my first language so I apologize if I have made some mistakes here.
thank you very much.
 
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