Commentary for I Kings 1:10

And his brother Shlomo, he did not invite. For he knew that the prophet had prophesied about him that he would reign.

He did not call Solomon his brother to eat with him because he knew that he would be opposed to him, being certain that he will become king after David his father. This was likewise the reason he did not call Nathan the prophet, because he prophesied to David that Solomon would rule after him, as was mentioned in Chronicles. (1 Chronicles 17:11) And in general he did not call those that would assent to his counsel like Zadok the priest, Benaiah son of Johoiada, Nathan the prophet, Shimei, Rei, and the mighty men that belonged to David because he knew that they would confound his counsel and, as a result, renew the hatred of the people who had agreed to his plan.