SE-SKOLORNAS 2016 Problem 6

Each cell in a $13 \times 13$ grid table is painted in black or white. Each move consists of choosing a subsquare of size either $2 \times 2$ or $9 \times 9$ , and painting all white cells of the choosen subsquare black, and painting all its black cells white. It is always possible to get all cells of the original square black, after a finite number of such moves ?