On a $5\times 5$ grid $\mathcal A$ of integers, each with absolute value $<10^9$, define a flip to be the operation of negating each element in a row / column with negative sum. For example, $(-1,-4,3,-4,1) \to (1,4,-3,4,-1)$. Determine whether there exists an $\mathcal A$ so that it's possible to perform $90$ flips on it. Alex Chen