nous nous sommes brossé

Bonjour Bill,

There is agreement with reflexive verbs only when the reflexive pronoun is the direct object.

Nous nous sommes lavés. - We washed up. The reflexive pronoun nous is the direct object: we washed ourselves -  the people doing the washing and being washed are the same.

But in nous nous sommes brossé les cheveux, the reflexive pronoun is actually the indirect object, because the direct object is les cheveux. While not grammatical, you can get a better sense of this by rewording the sentence: Nous sommes brossé les cheveux à nous. Since the direct object does not precede the verb, there is no agreement.

As this is a very tricky grammar point, Aurélie is going to address it in detail, either in this lesson or a separate one, but in the meantime you might find section 3 of this lesson helpful: Agreement with pronominal verbs