C182 INSTRUCTOR AND TRAINEE HAD L BRAKE LOCK UP ON LNDG. ACFT LEFT RWY.

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ON SEP/XA/98 APPROX XX30 I WAS APCHING RWY 35 IN CARTHAGE LAKE COUNTY ARPT; MS (25 NM NE OF JACKSON; MS) UNDER SQUAWK CODE VFR FROM JAN APCH ON 123.9 FREQ. AS I WAS LNDG THE ACFT; THE L BRAKE LOCKED UP AND THE PLANE SKIDDED TO THE L OFF OF THE RWY. TO BRING THE PLANE UNDER CTL; I LIFTED THE NOSE UP AND APPLIED FULL BRAKES UNTIL THE PLANE STOPPED. THE ELT CAME ON. I SHUT DOWN THE ENG AND INSPECTED THE PLANE. THE PLANE DIDN'T HAVE ANY DAMAGE. I TAXIED THE PLANE BACK ON THE RWY AND ONTO THE LCL RAMP. I CHKED THE BRAKES ON THE PLANE AND EVERYTHING SEEMED TO BE WORKING PROPERLY. I CALLED OPS FROM THE LCL PAY PHONE TO INFORM THEM OF THE SIT. I REQUESTED INFO ON HOW TO HANDLE THIS MATTER. I WAS TOLD TO RETURN TO THE MADISON ARPT (NBO); MS; IF EVERYTHING WAS IN LINE. THEY GAVE ME A NEW SQUAWK CODE AND I PROCEEDED TO MADISON ARPT (NBO); MS. WHEN LNDG; THE L BRAKE LOCKED UP AGAIN. THE PLANE SKIDDED TO THE L FOR THE SECOND TIME. I FOLLOWED THE SAME PROC AS I DID AT CARTHAGE ARPT EARLIER THAT SAME DAY AND STOPPED THE PLANE WITH NO DAMAGE OCCURRING.