"the verb must agree with the gender and number of the person."
Can you please explain the discrepancy between these two sources of information? Thanks.
I believe you are confusing the verb with the past participle. Let's take a look:
Alice s'est bien amusée. -- Alice had a lot of fun.
The verb is "est", which is the third person singular and hence agrees with Alice, the subject. The verb always needs to agree with the subject of the sentence, no matter what.
The participle in the example is "amusée". In the case of composite tenses which have être as their conjugated verb (as in this example), the participle needs to match the verb in number (singular) and gender (female), therfore you use "amusée".
Jean et Marc, vous vous êtes bien amusés?
Another example of the same kind: Jean et Marc are the subject in the second person plural and hence referred to as "vous". The verb (êtes) is matched to it. In the particular case of passeé composé with être as the conjugated verb, the participle needs to match the subject in gender and number: amusés. Another example, this time with avoir instead of être as the conjugated verb.
J'ai mangé du pain. -- I ate some bread.
Again, the verb "ai" is matched to the subject "je". The past participle "mangé", however, is not matched because the conjugated verb is avoir and not être.
With this clarification you should be able to reconcile the two explanations.
-- Chris (not a native speaker).
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