If B-1 commits an intentional personal foul against A-1 and A-1 is awarded two free throws, is the official's decision correct?

The official's decision to award A-1 two free throws after being intentionally fouled by B-1 is indeed correct. In basketball, an intentional personal foul is considered a serious breach of the rules as it is a deliberate attempt to disrupt the play without making a legitimate attempt to play the ball. When such a foul occurs, the player who was fouled is typically awarded free throws.

In the scenario described, since B-1 committed an intentional personal foul, the rules state that the fouled player, A-1, is entitled to two free throws. This rule is designed to penalize the team that commits the intentional foul and provide an opportunity for the fouled player to score points without interference from the defense.

Therefore, the decision to grant free throws to A-1 aligns with the established regulations in basketball regarding intentional fouls.