AN AC500 FLC LANDED ON THE WRONG RWY AT CLE.

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MISUNDERSTOOD CLRNC TO LAND EVEN THOUGH IT WAS REPEATED BACK. LINED UP ON WRONG SIDE OF RWY AND WAS ALLOWED TO CONTINUE FOR WRONG SIDE OF RWY LNDG. NO NOTIFICATION WAS GIVEN BY THE TWR FOR A 2 MI FINAL APCH. THERE WERE NO ACFT IN THE VICINITY OF THE AREA. TWR NOTIFIED WRONG RWY ONLY AFTER THE ACFT LANDED. SUPPLEMENTAL INFO FROM ACN 433556: THE PROB AROSE WHEN TWR SAID TO THE PIC THAT HE HAD LANDED ON RWY 23L INSTEAD OF RWY 23R. THE CONTRIBUTING FACTOR FOR THE OCCURRENCE HAD TO BE LACK OF ATTN. I TRUSTED HIM COMPLETELY; I WAS NOT EITHER ASKED BY HIM WITH THE DUTY OF THE FLT CTLS; OR THE RADIO COMS; SO TO KILL TIME; I WAS LOOKING AT THE ACFT MANUAL. THE NEXT THING I KNOW; TWR WAS SAYING THAT HE HAD LANDED ON THE WRONG RWY. I GUESS TWR ALSO MADE THE MISTAKE OR NOT TELLING HIM HE WAS ON FINAL FOR THE WRONG RWY; AND ALSO I MADE THE MISTAKE OF NOT PAYING ATTN. I COULD NOT BELIEVE HE HAD DONE IT. THE FAA REPRESENTATIVE ASKED FOR MY PLT CERTIFICATE; MEDICAL CERTIFICATE; AND SIC 135 CHK RIDE. I'M WORRIED BECAUSE THE FAA HAS A COPY OF MY SIC CHK RIDE; AND MY PLT'S LICENSE NUMBER.