The flight crew inadvertently retracted the landing gear during the landing rollout. The pilot under instruction (PUI) and the certified flight instructor (CFI) had both confirmed that the landing gear indicator lights were illuminated, and visually confirmed the nose gear was extended by use of the airframe mirror. The pilots indicated that after touchdown the right wing started to drop, and the CFI took the controls but the airplane veered off of the runway. As the pilots secured the airplane, they both observed the landing gear activation switch in the retracted position. During the recovery of the airplane the landing gear was extended, retracted, and then extended again. No damage to the landing gear locking mechanism was observed. The safety officer of the flight academy interviewed the flight crew and the recovery personnel. After the interviews it was determined that during the landing rollout and subsequent take-off roll, one of the crewmembers inadvertently placed the landing gear selector in the "up" position.