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latin squares turn to each other

Source: Iranian Third Round 2020 Combinatorics exam Problem3

November 18, 2020
latin squarescombinatorics

Problem Statement

Consider a latin square of size nn. We are allowed to choose a 1×11 \times 1 square in the table, and add 11 to any number on the same row and column as the chosen square (the original square will be counted aswell) , or we can add −1-1 to all of them instead. Can we with doing finitly many operation , reach any latin square of size n?n?
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