MathDB

Suppose a

m \times n

table. We write an integer in each cell of the table. In each move, we chose a column, a row, or a diagonal (diagonal is the set of cells which the difference between their row number and their column number is constant) and add either

+1

-1

to all of its cells. Prove that if for all arbitrary

3 \times 3

table we can change all numbers to zero, then we can change all numbers of

m \times n

table to zero.
(Hint: First of all think about it how we can change number of

3 \times 3

table to zero.)

Problem Statement