Question 55
A positive integer is written in each $1 \times 1$ cell of a rectangular board. The following two steps are allowed:
i) the numbers in the cells of an arbitrarily chosen row are multiplied by $2$;
ii) the numbers in the cells of an arbitrarily chosen column are decreased by $1$.
Is it possible after finite repetition of steps i) and ii) to get a board only with zeroes?
i) the numbers in the cells of an arbitrarily chosen row are multiplied by $2$;
ii) the numbers in the cells of an arbitrarily chosen column are decreased by $1$.
Is it possible after finite repetition of steps i) and ii) to get a board only with zeroes?