kesshin.

[lime tangle]

Please be patient

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[chilly fossil]

devrait-elle is should she

what are the first words in the middle list?

and tableau isn't table afaik

[foggy narwhal]

its not just "should" with a gender marker?

La musique devrait-elle être considerée comme une matière fondamentale au même titre que les mathematiques?

[chilly fossil]

uhm that's a bit complicated

so that's a question made with inversion, which is really formal in french

but in french you can't put the subject after the verb if it's not a pronoun, so we add that elle to stand for la musique

if the declarative sentence used a pronoun in the first place it'd be like:
Elle devrait être considerée comme une matière fondamentale au même titre que les mathematiques.
=> Devrait-elle être considerée comme une matière fondamentale au même titre que les mathematiques?

so you can see it's very similar to how english forms questions
but again that's the formal-sounding way