Kidner (1975: 392): "Those who deny David's authorship of the psalm on the ground that the psalm reads like an enthronement oracle curiously miss the point. It is just an oracle. What is unique is the royal speaker, addressing this more - than - royal person." No king of Israel was ever so close to God that he could normally be described, even metaphorically, as sitting at God's right hand. Terrien (2003: 752) terms this "stupendous for the Hebrew mind," suggesting an "exceptional degree of intimacy between God and the new monarch." The triumph over the king's enemies as he is arrayed in holy majesty (110:2-3) can possibly be taken of an earthly Davidic king, but 110:4 returns to language that seems highly inappropriate even for one as exalted as David (so also Carson 1984: 467). This "king" embodies an eternal priesthood (110:4), whereas legitimate Israelite kings in the line of David came from the tribe of Judah, not the tribe of Levi, from whom priests had to descend. And in 110:5 Yahweh is said to be at this king's right hand, rather than vice versa, as if God and king were interchangeable! Finally, this monarch will do what God alone is described elsewhere as doing: judging the nations and crushing the rulers of the whole earth (110:6) For all these reasons, B. C. Davis (2000) concludes that the psalm is purely messianic. -taken from Commentary on the New Testament Use of the Old Testament by G.K Beale and D.A. Carson, section on Matthew 22.

Jesus was claiming that he was going to enter permanently into the heavenly Holies of Holies and sit down. Jesus might as well have claimed that he owned the place! Indeed, that is what his statement amounted to. As Darrell Bock has put it, Jesus' claim "would be worse, in the leadership's view, than claiming the right to be able to walk into the Holy of Holies in the temple and live there!"
...when Jesus alluded to Daniel 7:13 and Psalm 110:1 in his response to Caiaphas's question [in Mat. 26]...Jesus was claiming to be a heavenly, divine figure who would be seated at God's right hand, exercising divine rule forever over all people everywhere.
...What Jesus does in fusing Psalm 110:1 with Daniel 7:13 is unique and results in a claim that goes far beyond anything said about the Son of Man in Enoch. -taken from Putting Jesus in His Place: The Case for the Deity of Christ by Robert M. Bowman Jr. and J. Ed Komoszewski, p. 243-45, 252

First, he [Rabbi Singer] is INCORRECT in stating that "my Lord" is reserved "for the profane, never the sacred." Just look in Joshua 5:14, where Joshua addresses the angel of the Lord as "my lord" ('adoni). Yet this divine messenger is so holy that Joshua is commanded to remove the shoes from his feet because he is standing on holy ground, just as Moses was commanded when the angel of the Lord - representing Yahweh himself - appeared to him (Exod. 3:1-6). This is hardly a "profane" rather than "sacred" usage! Similar examples can be found in Judges 6:13 and Zechariah 1:9, among other places...
...Second, Singer's WHOLE ARGUMENT HINGES ON THE MASORETIC VOCALIZATION, which did not reach its final form until the Middle Ages. As every student of Hebrew knows, BIBLICAL HEBREW WAS WRITTEN WITH CONSONANTS AND "VOWEL LETTERS" ONLY; the VOWEL SIGNS were added hundreds of years later. Yet both 'adonai (used only for Yahweh) and 'adoni (used for men and angels, as we just noted) are SPELLED IDENTICALLY IN HEBREW, consisting of the four consonants '-d-n-y. How then can Rabbi Singer make such a dogmatic statement about the differences between these two forms in the Bible? His argument stands only if we accept the absolute authority of the Masoretic vocalization, which in some cases follows the original Hebrew by almost two thousand years [footnote] 277.
...Third, it is not really important whether we translate with "my Lord" or "my lord", since Yeshua's whole argument [in Mat. 22] was simply that David called the Messiah "lord", meaning that the Messiah had to be more than David's son.
...[Footnote] 277: ...Interestingly, 'adonai (with qametz) in Judg. 6:15 is rendered with "my lord" in the LXX (kyrie mou) as opposed to simply Lord (kyrie, as it is usually rendered with reference to Yahweh), a rendering possibly reinforced by Judg. 6:13, with 'adoni. This, then, could point to a change in the Masoretic vocalization of 'adoni. -taken from Michael L. Brown's, Answering Jewish Objections to Jesus, vol. 3, Messianic Prophecy, section 4.29. Emphasis mine.

http://www.hebrew4christians.com/Names_of_G-d/Yeshua_is_Adonai/yeshua_is_adonai.html

http://impedingbalaam.blogspot.com/2010/12/psalm-110-and-anti-missionaries.html