RWY INCURSION BY A CE525 FLT CREW DURING TAXI TO RWY 24L AT CLE; OH.

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JUST HAD CLRED CUSTOMS AT GATE. MY FO WAS GETTING CLRNC AND TAXI INSTRUCTIONS. I WAS DOING POST-START; PRE-TAXI CHKLIST. BAD SIDE-TONE; I WAS UNABLE TO HEAR HIS READBACK. HE TOLD ME; 'RWY 24L VIA TXWY W; RWY 24C; R TURN TXWY Z HOLD SHORT OF RWY 24L.' MADE L TURN FROM GATE; STOPPED SHORT OF RWY 24L. HE INSISTED CLRED TO CROSS RWY 24L (ACTIVE RWY) R RWY 24C; TXWY Z; R TURN HOLD SHORT RWY 24L. PROB AROSE BY ME ACCEPTING FO'S INSTRUCTIONS -- NOT QUESTIONING HIS INSISTENCE TO CROSS RWY 24L. RETROSPECT; DOES NOT MAKE SENSE. HOW ABOUT; 'RWY 24L VIA TXWY W; HOLD SHORT.' HE CLAIMS CLRNC WAS; 'RWY 24L VIA TXWY W; R RWY 24C; R TXWY Z HOLD SHORT RWY 24L.' DISCOVERED WHEN GIVEN PHONE NUMBER TO CALL; I CALLED BACK ON GND; WHEN INFORMED; 'LOOKS LIKE YOU CROSSED ACTIVE RWY;' TOLD BOYS TO HOLD TAPES. CONTRIBUTING FACTORS: OVERAGGRESSIVE FO. I PUT TOO MUCH TRUST IN THIS GUY. I DID NOT HEAR HIS READBACK. CORRECTIVE ACTIONS: CAPT ALWAYS WILL LISTEN AND COPY DOWN ALL CLRNCS. ALSO HAVE ARPT TAXI CHART IN HIS POSSESSION.