Adam, and did not run after her own ways, but submit as becoming "ONE" with her husband, God blessed their union.
 
Seeing that it was Adam who gave His wife the name, and Eve who came out of a rib of her husband, it was fitting that she "belong" to him, and be under his authority and care.  This was established in the beginning.

God said that Adam's WIFE would bring forth children in sorrow and have her HUSBAND to rule over her.  Yet in this bringing forth of children, she would bruise the head of the adversary.  Set from the beginning, she was under authority, yet a part of God's plan for salvation of man.

16: Unto the woman he said, I will greatly multiply thy sorrow and thy conception; in sorrow thou shalt bring forth children; and thy desire shall be to thy husband, and he shall rule over thee.

Genesis 3:15: And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.

He did not mean with this command, that every man had authority over every woman.  Indeed the scripture teaches, "Let a woman be in subjection to her OWN husband".

6:a Even as Sara obeyed Abraham, calling him lord: whose daughters ye are…

As with Adam's wife, so with New Testament Church women, submission to their own husbands was the order of the day, yet to the kingdom of God, she still had great things to offer.

Many young wives today do choose to "teach" and take away the rightful authority of the husband, going as far as to divorce their authority if they do no agree with his leadership.  Neither the scriptures nor our Lord and Savior Jesus Christ teach that any woman has that kind of authority.  Marriage is a type of Our Lord and his church, who must always be in submission to Him.

But of natural matters and commands, the woman Eve was deceived by satan then as well.

However, The Prophetess Deborah was not deceived in the work of God, neither was Anna, this is an important distinction.