100691 – We Solve Problems

#### Invariants , Invariants and semi-invariants

There are real numbers written on each field of a $m \times n$ chessboard. Some of them are negative, some are positive. In one move we can multiply all the numbers in one column or row by -1. Is that always possible to obtain a chessboard where sums of numbers in each row and column are nonnegative?

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