Flight Instructor reported a gear up landing while performing recurrent training. The aircraft had recently come out of an annual inspection and the gear warning system had not been confirmed operational before landing.

Narrative

We conducted a formal re-currency flight using a specific curriculum. The owner was PIC (pilot in command) and had over 2000 hours of retractable gear time. They had owned subject aircraft for several years. Our flight took off from ZZZ and we performed curriculum maneuvers for about 1.5 hours. All satisfactory. The first landing at ZZZ1 was excellent. I decided on a short field take off and landing for the next maneuver. After takeoff; I asked the owner to pick the touchdown spot while on downwind. The owner landed on the touchdown spot but with the gear up. We never heard a gear warning alarm. In retrospect; we were both distracted by selection and concentrating on the touchdown spot when we should have put gear down first; however; we did not get a gear alarm. The airplane had received an annual recently and I believe the gear warning should have been checked during the annual inspection. I would suggest that when an instructor gets into a retractable; they should confirm that the gear warning alarm is operational before attempting a landing. Also be sure the gear is down before distracting the PIC; or if you want to distract him; don't distract yourself at the same time.