Question 9: The square in the left figure below is divided into nine cells. In each cell, we write one of the numbers -1, 0, and 1 Use the Pigeonhole Principle to prove that, among the rows, columns, and main diagonals, there exist two that have the same sum. For example, in the right figure below, both main diagonals have sum 0. (Also, the two topmost rows both have sum 1, whereas the bottonm row and the right column both have sum -2.) 1-1 -1 0-1