Is the husband required to ask his wife's permission before leaving the house, and what is the ruling of Islam on this matter?

A wife must seek her husband's permission when leaving the house, but a husband does not need to seek his wife's permission. The husband's right over her is greater than her right over him, because Allah Almighty says: "But men have a degree over them," and because the Prophet, peace and blessings be upon him, said: "If I were to command anyone to prostrate to another, I would have commanded women to prostrate to their husbands." The man is responsible for providing for and maintaining the family, and the woman's work is in her home. There is no harm if the husband informs his wife when he leaves, out of affection and love, not out of obligation.