One spouse can give another the power to represent them as their agent. The relationship of married persons, or of de facto spouses, does not preclude them or other family members from appointing each other as their agents.
In addition to this, the common law presumes that spouses, or de facto spouses who are living together, are each other's agents for the purposes of acquiring necessities. This agency power arises by law, without any need for agreement. However, this common law presumption has been abolished by statute in some jurisdictions.