Yes. Not too hard to confirm with a tiny little program:

    lockers = ['Closed'] * 101
    for i in range(1, 101):
      for locker in range(i, 101, i):
        lockers[locker] = 'Open' if lockers[locker] == 'Closed' else 'Closed'

    print ([locker for locker, value in enumerate(lockers) if value == 'Open'])

    >>> [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]