It is undeniable that Martin Ødegaard is a player who is quite influential in Arsenal's midfield so of course with the absence of Martin Ødegaard will make Arsenal's team performance a little different even though Arteta still has many other options to fill the gap. Martin Ødegaard has an ankle injury which is predicted to not take long to recover from this injury so I think if that is the case there will be no major impact on the team as long as their influential player does not suffer a long-term injury.
Arsenal's squad without Martin Ødegaard is not complete, and I don't think that Arsenal has great players on the bench who can replace him and perform as well as he does in midfield. His injury is a bad thing for Arsenal because it will surely affect their performance. Anyone who regularly watches Arsenal matches knows that Martin Ødegaard is one of their great players, doing an excellent job in the squad.
Now it's up to Arteta. With Martin Ødegaard absent from the squad, Arteta has some work to do. He needs to carefully consider who will take that position, as it requires thoughtful decision-making. I can't say much about Arsenal's next match, but I don't have confidence that they will be able to win, especially with Rice also absent. Without Ødegaard, the squad may struggle and look disorganized. In my view, for the next one to three matches, Arsenal will likely find it hard to perform as expected.