Regarding the fact that Aircraft A entered the runway, it is probable that when the PIC A received the ATC instruction, he mistook the Towerfs instruction to hold short of runway as the instruction to line up and wait, and his misunderstanding was not corrected.It is probable that the reason why the PIC Afs misunderstanding was not corrected is because the PIC A and the FO A did not cross-check the ATC clearance, as specified in the Company Afs manual.