Theophylact of Ohrid

The Lord commanded us to love one another with true affection. When? When He said: "as you wish people to treat you, so treat them also" (Luke 6:31). If we love for our neighbors to have true and guileless affection toward us, then we ourselves must have exactly the same affection toward them. And since this is the Lord's commandment, when we abide in Him, all the more He grants us Himself. …

Commentary on 1 John ↗

Oecumenius

And this is His commandment: that we should believe on the name of His Son Jesus Christ. And what commandment do we keep? That which says: Have mutual love among yourselves. (Jn. 13:35) Therefore, since we have received the command to love one another with the faith that is in the name of His Son Jesus Christ, we have done this; through this we know that the grace He has given us through His Spirit is firmly established in us. …

Commentary on 1 John ↗

Augustine of Hippo

And what are those commandments? "This," saith he, "is His commandment, That we should believe on the name of His Son Jesus Christ, and love one another." Ye see that this is the commandment: ye see that whoso doeth aught against this commandment, doeth the sin from which "every one that is born of God" is free. "As He gave us commandment:" that we love one another.

Ten Homilies on 1 John 6 ↗

Bede

And this is his commandment, that we believe in the name of his Son Jesus Christ, etc. He placed the commandment in the singular number and subsequently added mandates to it, namely faith and love, because clearly these cannot be separated from each other. For neither can we rightly love one another without faith in Christ, nor can we truly believe in the name of Jesus Christ without fraternal love. And he says, let us love one another, as he gave commandment to us. …

Commentary on the Catholic Epistles ↗