This is kind of a part II on the subject of authority (part I). Specifically, we have a perfect model for us in our understanding of authority within the Trinity itself.
Christian thinkers since the very early church have asserted the doctrine of the Trinity, that God is One in Three and Three in One. He is One in a sense and Three in a different sense. We cannot understand this, in the sense of getting our heads all the way around it. But we can assert what the Scriptures assert. God is One in the sense of His essence or being. There is but one God. But this one God eternally subsists in three Persons, three centers of consciousness. We know that the Son is aware that He is not the Father, and the Father knows that He is not the Son. They are distinct. They are all equally God, equally in possession of the single divine Essence. They are all equally powerful, knowledgeable, everywhere present and perfect in every sense.
But there is distinction of the Persons. They are aware of one another and that they are not each other. And there is also distinctions among them as to their works and acts. The Trinity always does what it does as a perfect Unity, but the Persons of the Trinity engage in the work of God in distinct ways.