Genesis 2:15 And the LORD God took the man, and put him into the garden of Eden to dress it and to keep it.
The word "keep" is the KJV translation of "shomer". It is keep in the sense of "guard" as in the KJV Genesis 39:21 (keeper of the prison) or in KJV Acts 12:6 (he keepers before the door kept the prison) or in Acts 16:27 (the keeper of the prison).
Adam was told to tend and keep (guard) the garden (Gen 2:15). He should have used this authority to guard the garden from the enemy.
Man in God's image was designed to express dominion just like God - by speaking WORDS of faith and authority (thats how we dominate the devil today - by our WORDS).
However rather than speaking God's word to Satan - dominating him and sending him away, Adam submitted to Satan's words and came under the curse (the dominion of darkness). Satan became the god of this world after Adam had handed him his authority. (Satan maintains his dominion if he can deceive man into thinking and speaking and speaking his thoughts of hate, bitterness etc).
So Adam lost his dominion over Satan, but praise God, the Second Adam (Jesus) came. He was untainted by sin. He said that the devil had nothing in Him and no power over Him. He showed us what it was like to walk in DOMINION. He demonstrated how man was meant to live. He dominated demons, casting them out with a word. He rebuked sickness and it fled. He even rebuked winds and calmed the tumultuous waves of the sea with His WORDS.