Charles Ellicott Commentary 1 Kings 2:13

"Then Adonijah the son of Haggith came to Bath-sheba the mother of Solomon. And she said, Comest thou peaceably? And he said, Peaceably." — 1 Kings 2:13 (ASV)

And Adonijah ... came. —Adonijah's request to Bathsheba, and the signs of honour paid to her by the king—of which there is no trace in her approach to David's presence (1 Kings 1:15–16; 1 Kings 1:28; 1 Kings 1:31)—illustrate the universal custom of Eastern monarchies, where, while the king's many wives are seldom considered to be of great political importance, the mother of the reigning king is a person of great dignity and influence. We may notice how constantly the name of each king’s mother is recorded in the history.