Nine lightbulbs are arranged in a \(3 \times 3\) square. Some of them are on, some are off. You are allowed to change the state of all the bulbs in a column or in a row. That means all the bulbs in that row or column that were initially off now light up, and the ones that were initially on, now go dark. Is it possible to go from the arrangement in the left to the one on the right by repeating this operation?