Rashi on TanakhLeviticus 9

It was on the eighth day — of the installation. That [was] Rosh Chodesh Nison, that very day on which the Tabernacle was set up, and it [= that day] took [the] ten crowns which are taught in Seder Olom.

and to the elders of Israel to announce to them that [it was] by Divine command [that] Aharon entered [the Tabernacle] and served in the high priesthood, that they not say that he had entered into it on his own authority.

Take, for yourself, a young calf, to let [Aharon] know that God forgave him by means of this calf for the deed of the [Golden] Calf which he had made.

for today Adonoy will appear to you — to rest His Shechinoh on the work of your hands; that is why these sacrifices are obligatory for this day.

Approach the altar. [It was because] Aharon was ashamed and afraid to approach. Moshe said to him: Why are you ashamed? [It was] for this that you were chosen!

Your sin-offering, a young calf.

And your burnt-offering, the ram.

The people’s offering, the kid of goats, young calf and lamb. Wherever it states “ עֵגֶל “ (a calf), [it refers] to a yearling, and from here you learn [this rule].

The flesh and the skin, etc. We do not find an “outer” sin-offering that is burned except this [one] and that of the installation, and all of them by Divine command.

[Aharon’s sons] presented, an expression [denoting] “handing over” and “preparation.”

And offered it a sin-offering, [that is, וַיְּחַטְּאֵהוּ means:] He treated it according to the rule of a sin-offering.

As the first one, as his [own] calf.

He did it according to the rule, [the rule] explained in [regard to] a freewill burnt-offering in Vayikro 1.

He filled his palm from it. This is the קְמִיצָה [= separating the fistful].

Aside from the burnt-offering. All these he did after the daily burnt-offering.

The covering, [that is,] the fat covering the innards.

They put the fats on top of the breasts, after the “waving” the kohein [who did] the waving gave them to another kohein to burn them; [thus that which] was above was [now] below.

And he blessed them [with the blessing of] Birkas Kohanim — May [He] bless you, May [He] cause [His Face] to shine, May [He] lift up.

He descended from the altar.

Moshe and Aharon went [in]to, etc. Why did they enter? I found in the section of Millu’im, in the added בָּרַיְיתָא to our Toras Kohanim: Why did Moshe enter with Aharon? To teach him the ritual of the incense, or perhaps he entered for some other purpose? I can argue [as follows]: Descending and entering require a blessing, just as descending is similar to the [Temple] service, so entering is similar to the [Temple] service. Therefore you have learnt: Why did Moshe enter with Aharon? To teach him the ritual of the incense. Another interpretation: When Aharon saw that they offered all the sacrifices, and all the rituals had been performed, and [still] the Shechinoh did not descend for Israel, he was pained, and thought, “I know that God is angry with me and [it is] because of me that the Shechinoh did not descend for Israel”! He said to Moshe: “My brother Moshe, is this [what] you did to me, that I entered and was shamed”? Moshe immediately entered with him, and they begged for mercy, and the Shechinoh descended for Israel.

They went outside and blessed the people. They said: “’May the pleasantness of Adonoy our God be upon us.’ May it be [His] Will that the Shechinoh should rest on the work of your hands.” Because all seven days of the installation [during which time] Moshe set up the Tabernacle and served in it [as a kohein], and took it down every day — the Shechinoh did not rest on it, and Israel were ashamed, saying to Moshe: “Our master Moshe! All the trouble we went to [in order] that the Shechinoh should rest among us, and that we should know that we have achieved atonement for the sin of the [Golden] Calf. Therefore he said to them: “This is what Adonoy commanded you to do and the glory of Adonoy will appear to you. My brother Aharon is worthy and [even] more important that I, for by means of his sacrifices and his service the Shechinoh will rest among you, and you will know that the Omnipresent chose him.

They raised [their voices], according to its Targum.