À la page 28 dans Advanced French Grammar, V. Mazet présente ceci : Some pronomial verbs don't exist in a non-pronominal form. As a result, you can't determine if the pronoun se is a direct object ...
All verbs that take "être" as their auxiliary verb must agree in gender and number with the subject. This I know. But does this apply also to pronominal verbs? For instance, "Elle s'est rasée les ...