True, Eve was deceived, but there is no doubt that she knew God's command and chose to break it because she corrected the serpent on what God's command was.
Eve was deceived because Satan told her it would make her more like God and that she would not die. But there is no doubt that she knew God had commanded that it not be eaten and had said she would die. Her deception occured because she chose to listen to the serpent over the words of God that she knew.
Adam's authority couldn't have saved Eve. Eve had already eaten. Adam's choice was to either share in Eve's fate or let her face God's judgement alone. I don't know if Adam fully understood what God's judgement would be, but Adam chose to follow Eve in this.