BE76 RWY INCURSION. INSTRUCTOR AND STUDENT HAVE RWY INCURSION. INSTRUCTOR MISSES LAST PART OF TWR CLRNC AND STUDENT TAXIES ONTO TKOF RWY WITHOUT CLRNC.

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THIS WAS TO BE A LCL TRAINING FLT. TFC ON THE GND CTL FREQ AND TWR FREQ WAS VERY LIGHT. WE DID OUR RUNUP AND; WHEN COMPLETE; WE TAXIED UP TO HOLD SHORT LINE AND MADE OUR CALL TO TWR. TWR CTLR INFORMED US THAT RWY 21L WAS NOW CLOSED. TWR CTLR GAVE US (THE STUDENT AND MYSELF; THE INSTRUCTOR) INSTRUCTIONS TO TAXI ACROSS RWY 21L AND TAXI TO RWY 3L VIA TXWY C. RWY 21L WAS SUPPOSED TO BE CLOSED UNTIL LATER IN THE DAY. THIS DISTR ME AND I MISSED THE LAST 1/2 OF OUR TAXI INSTRUCTIONS. COMPLACENCY LED ME TO TRUST THE STUDENT WHO BEGAN TAXIING IMMEDIATELY. I SHOULD NEVER HAVE TRUSTED THE STUDENT TO GET THE INSTRUCTIONS CORRECT. THE STUDENT DID NOT UNDERSTAND THE INSTRUCTIONS; AS I LATER FOUND OUT. BEFORE I KNEW IT; WE HAD TAXIED ONTO RWY 3L. I DID NOT KNOW IF THIS WAS THE ACTIVE BECAUSE TWR WAS NOW DIRECTING OTHER TFC TO RWY 12. LATER I FOUND OUT THAT RWY 3L WAS NOT THE ACTIVE; BUT THAT IS NOT IMPORTANT. I SHOULD HAVE KNOWN WHAT THE TAXI INSTRUCTIONS WERE. THE STUDENT WAS A PVT PLT WORKING ON HIS MULTI-ENG RATING. UPON TAXIING ONTO RWY 3L; TWR CALLED US IMMEDIATELY TO RECTIFY MY ERROR.