Question 80
Given an $n \times n$ grid, we call two cells in it adjacent if they have a common side. At the beginning, each cell is assigned number $+1$. An operation on the grid is defined as follows: one chooses a cell, and then changes the signs of every number in its adjacent cells (but does not change the sign of the number in itself). Find all the integers $n \ge 2$, such that after a finite number of operations, all the numbers in the cells of the grid are changed to $-1$. (posed by Shen Huyue)