PA44 STUDENT AND INSTRUCTOR SUFFER GEAR COLLAPSE ON LNDG.

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MY STUDENT AND I HAD JUST DEPARTED; BEGINNING A VFR XCOUNTRY. MY STUDENT ALERTED ME THAT THERE WAS NO GEAR INDICATIONS AT ALL WHEN WE WERE 400 FT AGL; AND WHEN HE ATTEMPTED TO GET THE GEAR UP; NOTHING HAPPENED. I TOOK THE CTLS AND ASKED ADVISORY TWR TO SEE IF THE GEAR APPEARED DOWN FROM THE TWR'S POINT OF VIEW. WE DID A LOW APCH WHILE TWR VIEWED OUR LNDG GEAR WITH BINOCULARS. THEY SAID IT APPEARED TO BE DOWN SO WE WENT AROUND WHILE I CONTINUED TO RECYCLE THE GEAR AND HOPED FOR ANY INDICATION (PREFERABLY 3 GREEN LIGHTS). I SLOWED THE ACFT; AND AS WE TOUCHED DOWN; THE L MAIN GEAR COLLAPSED WHILE THE R MAIN AND NOSE GEAR STAYED DOWN AND LOCKED. WE MAINTAINED THE RWY CTRLINE AND EVENTUALLY CAME TO A COMPLETE STOP. THE ACFT WAS REMOVED FROM THE RWY; AND AS SOON AS THE MASTER SWITCH WAS TURNED ON; THE LNDG GEAR APPARENTLY DISPLAYED 3 GREEN LIGHTS AND THE L MAIN GEAR WENT DOWN AND LOCKED. I DEFINITELY LEARNED FROM THIS EXPERIENCE AND FEEL LIKE I COULD HAVE DONE MORE TO AT LEAST TROUBLESHOOT THE SITUATION MORE THOROUGHLY.