The following two verses ordain the sacrament of marriage.
“O virgin! O young maiden! I take thy hand i.e., I marry thy and thou marriest me for accomplishing the purpose of begetting children. Lady! Mayes thou grow old in my (thy husband’s) company and may I grow old in thy (my wife’s) company and may we, in
this way, lovingly perform our duties and remain happy. God, full of glory and grandeur, the ordainer of justice, the creator and supporter of the whole universe has bestowed thee on me for household duties. All the learned men assembled here are our witnesses. If any of us should ever violate this our compact he or she would be punishable by God and the learned.” Rig VIII.3.27.1.
As to how the husband and the wife should conduct themselves after going through the marriage, God ordains:
“O husband of the house-holder and may separation never take place between you and on account of quarrel or (permanent) residence in a foreign land. May you, by My blessing, always discharge your duties, do good to all, remain devoted to Me and live up to old age full of joys of various kinds. May you live happily
in your home in the company of your children and grandchildren, engaged in the performance of your duty and virtuous acts. Rig. VIII. 3-28-2
From this it is clear that one man should have only one wife and one woman only one husband. That is to say, the marriage of one man with many women and of one woman with many men is prohibited, because in all the Vedic verses only the singular number is used (for the husband or the wife.
There are many mantras in Vedas dealing with the subject of marriage.