Where is the place that produces the most ATP in cellular respiration

I thought it was in the matrix because protons flow through ATP synthase from inter membrane space in to it. However, my textbook says it's the inner membrane, so I'm confused.

Thank you ! =)

You've almost got it--when the H+ flow back into the matrix across that inner membrane, as long as they do it via the ATPase, their flow inwards is coupled to ATP formation. So, the action is really at the ATPase, which is located in the inner membrane. The electrochemical gradient between the higher concentration of H+ in the intermembrane space and the lower concentration in the matrix provides the driving force for the inward flow, but the ATPase is critical--if the ATPase is inhibited, or if one of the uncoupling proteins becomes active, you still can get proton flow inward, but there won't be any ATP made--i.e. that gradient and the resulting proton flow can be uncoupled from ATP production. So your textbook is correct.