IPA: //məˈdʒɪstəˌriːəli//
KK: /mædʒɪˈstɪrɪəli/
In a way that shows authority or importance; done with a commanding presence.
The judge spoke magisterially, making it clear that his decision was final.
Magisterially → It is formed from "magister" (from Latin, meaning master or teacher) and the adverbial suffix "-ially" (meaning in a manner relating to). The word "magisterially" means in a manner befitting a master or authoritative figure.
Think of a 'master' ('magister') acting in a way that shows authority — that's what 'magisterially' means.