Mutual exclusion is preserved. As each Pi enters its critical section only if flag[j] = false. If both processes can be executing in their critical sections at the same time, then flag[0]=flag[1]=true. These two observations imply that P0 and P1 could not have successfully executed their critical while statements at the same time, So mutual exclusion is preserved.

Pi can be prevented from entering the critical section only if it is stuck in the outer while loop with the condition flag[j]=true