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Is 一緒に needed in this case？
Or is it just ->> 行こう？
I think「一緒に」is necessary, but it will be better to say 「一緒に行きませんか」( if Aーさん isn't close to Bーさん) or「一緒に行かない？」( if B-さん is a friend). It's more polite.
Required, but never shown