The pilots reported that the instructional flight was the first leg of a multi-leg trip. Upon arrival at their initial destination, the landing gear selector was moved to the down position; however, the landing gear position lights indicated that the landing gear was not down and locked. Due to an absence of airport personnel to visually confirm the position of the landing gear, the instructor elected to divert to an airport with an air traffic control tower. Upon arrival, the air traffic controller reported that the nose and right main landing gear were extended; however, the left main gear was not. In an effort to extend the landing gear, the pilots attempted to troubleshoot the malfunction. They performed the emergency gear extension procedure, and multiple flight maneuvers to force the landing gear down, without success. The pilots also noted that the landing gear motor circuit breaker was open and would not reset. After consulting with maintenance personnel, they elected to delay landing, in an attempt to reset the circuit breaker, preferring a gear up landing rather than a partial landing gear extension that could result in a loss of control. The circuit breaker was subsequently reset, and the landing gear was retracted in preparation for a gear up landing. The pilots confirmed with air traffic control that all three landing gear were retracted; however, the left main gear door remained “ajar.” An uneventful gear up landing was conducted, which resulted in substantial damage to the underside of the fuselage. A postaccident examination of the airplane by an FAA inspector revealed abrasion damage to the left inboard landing gear door, damage near both of its hinges, and a failed aft hinge, consistent with the open door contacting the runway during landing. In addition, the actuator rods that mechanically connect the landing gear motor gearbox to the left main landing gear and left inboard door had failed. The left main landing gear was likely unable to extend due to the failed actuator rods; however, it could not be conclusively determined which actuator rod failed first.