Yes. We must admit equality among the divine persons because if there were any inequality in the divine persons, they would not have the same essence (and thus the three persons would not be one God, which is impossible).
Athanasius says that "the three persons are co-eternal and co-equal to one another."
In the divine persons there is nothing for us to consider but the essence which they have in common and the relations in which they are distinct. Now equality implies both --namely, distinction of persons (for nothing can be said to be equal to itself) and unity of essence (since for this reason are the persons equal to one another, that they are of the same greatness and essence).
Now it is clear that the relation of a thing to itself is not a real relation. Nor, again, is one relation referred to another by a further relation: for when we say that paternity is opposed to filiation, opposition is not a relation mediating between paternity and filiation. For in both these cases relation would be multiplied indefinitely.
Therefore equality and likeness in the divine persons is not a real relation distinct from the personal relations: but in its concept it includes both the relations which distinguish the persons, and the unity of essence.