A more thorough explanation:

Matrimonial cohabitation refers to the living together of a married couple. It suggests that they are partners in life and may engage in sexual relations.

For example, when a husband and wife live together in the same house, they are in a state of matrimonial cohabitation. They share their lives and their home, and they may have children together.

Matrimonial cohabitation is different from illicit cohabitation, which refers to unmarried couples living together in a way that is questionable on grounds of social propriety. This type of cohabitation may be considered lewd or lascivious, especially if the couple engages in sexual intercourse.

Overall, matrimonial cohabitation is a legal and socially acceptable way for married couples to live together and build a life together.