“Solomon sat on the throne.” The Bible never says how old Solomon was when he became king, but for reasons why he seems to have been 20 or a little older, see commentary on 1 Kings 3:7. Also, it was common when a king began to reign that the Bible stated whether he did what was evil or what was right in the eyes of Yahweh (cp. 2 Kings 13:1-2, 10-11; 14:23-24; 1 Kings 15:11; 2 Kings 12:2; 14:1-3). However, the Bible does not say that about Solomon. It does say that Solomon disobeyed God concerning his material wealth and where he got it, and he also became an idolator later in his life (1 Kings 10:14-11:13). The Bible does say how long Solomon reigned: 40 years (1 Kings 11:42).
“and his kingdom was firmly established.” This is also stated in 1 Kings 2:46, and the two verses, 1 Kings 2:12 and 2:46, form a kind of inclusio, an enclosing envelope that surrounds and groups the accounts between them. Between the two verses are four accounts of Solomon dealing with potential enemies. He deals with his older brother Adonijah, an unfaithful priest Abiathar, Joab, one of David’s generals who supported his rival and not Solomon, and Shemei, a man from the tribe of Benjamin who showed up as a disobedient and threatening subject. On a macro scale, this inclusio seems to very much be a kind of type of the start of the Messianic Kingdom of Christ. When Christ conquers the earth and sets up his kingdom he will separate the “goats,” people who have not supported him or his people, from the “sheep,” people who have supported him, and have the goats thrown into the Lake of Fire for destruction (Matt. 25:31-46, see commentary on Matt. 25:31 and Matt. 25:32). One of the things that makes a kingdom safe and prosperous is getting rid of potential internal rebellion and strife, and Christ will do that and then rule his kingdom with a rod of iron.