Objection 1. It would seem that in the state of innocence man would not have had mastership over all other creatures. For an angel naturally has a greater power than man. But, as Augustine says (De Trin. iii, 8), "corporeal matter would not have obeyed even the holy angels." Much less therefore would it have obeyed man in the state of innocence.
Objection 2. Further, the only powers of the soul existing in plants are nutritive, augmentative, and generative. Now these doe not naturally obey reason; as we can see in the case of any one man. Therefore, since it is by his reason that man is competent to have mastership, it seems that in the state of innocence man had no dominion over plants.
Objection 3. Further, whosoever is master of a thing, can change it. But man could not have changed the course of the heavenly bodies; for this belongs to God alone, as Dionysius says (Ep. ad Polycarp. vii). Therefore man had no dominion over them.
On the contrary, It is written (Genesis 1:26): "That he may have dominion over... every creature."
I answer that, Man in a certain sense contains all things; and so according as he is master of what is within himself, in the same way he can have mastership over other things. Now we may consider four things in man: his "reason," which makes him like to the angels'; his "sensitive powers," whereby he is like the animals; his "natural forces," which liken him to the plants; and "the body itself," wherein he is like to inanimate things. Now in man reason has the position of a master and not of a subject. Wherefore man had no mastership over the angels in the primitive state; so when we read "all creatures," we must understand the creatures which are not made to God's image. Over the sensitive powers, as the irascible and concupiscible, which obey reason in some degree, the soul has mastership by commanding. So in the state of innocence man had mastership over the animals by commanding them. But of the natural powers and the body itself man is master not by commanding, but by using them. Thus also in the state of innocence man's mastership over plants and inanimate things consisted not in commanding or in changing them, but in making use of them without hindrance.
The answers to the objections appear from the above.
Source: Summa Theologica (New Advent)