Motion in an expanding space

As there is no friction or gravity to mess with B won’t it continue to wards A at the same rate, and the expansion will continue at the same rate because their relative separation doesn’t change. Therefore won’t A&B maintain the holding pattern?(please note I failed o level math first time round and anything to do with numbers hurts my head, more of a pictures guy)

yes, the balloon analogy.Take a balloon and draw lots of dots on the surface. Now blow the balloon up slowly.You will notice that as the balloon expands all the dots move apart from each other. Take any dot and each one will see that all others are moving away from it at different speeds. Yet none are the centre of this expansion.