CMO 1992 Problem 3

Given a $9\times 9$ grid, we assign either $+1$ or $-1$ to each square on the grid. We define an adjustment as follow: for each square on the grid, we make a product of all numbers of those squares which share a common side with the square (excluding itself).Then we have $81$ products. Next we replace all the squares' values with their corresponding products. Determine if we can make all values in the grid equal to $1$ through finite adjustments.