Inversion is described as 'the more formal way' and also as 'the more elegant way'. Please clarify.

In French, like in all languages, there are different ways to say the same thing, depending on the setting in which you find yourself. For example, when talking to your brother you would say, "Hi, what's up, bro! It's awesome you came to visit me!" To express the same intention but toward the President of the US, you would formulate it differently: "Good morning, Mr. President" I am certainly delighted you could come and visit me!"

The same holds true in French. Usually, the inverted form of formulating a question is considered more formal:

Comment vous-appelez-vous? -- What is your name? (formal register)
Tu t'appelles comment? -- What is your name? (familar register)

Here is a more in-depth link to an article discussing registers in the French language: https://www.lawlessfrench.com/linguistics/register/

-- Chris (not a native speaker).

Thanks Chris, I had thought of 'elegant' and 'formal' as being quite different in meaning but I now see, in this context, that they have a similar meaning.