Inversion after negative expressions and 'only...'

I have tried to learn English via the BBC, which is great! I like your Quiznet, but I need an explanation for the fifth item of Quiz Three: 5. Choose the correct answer:

Only at night ..... the safety of their cave

bats leave 

bats will leave

leave bats

do bats leave

Why is it not possible to use 'bats leave'? I would like to acquire this grammatical rule.

 Quite often in English, certain expressions with a restrictive or negative meaning are placed at the beginning of a sentence. The reason for doing so is to emphasize the point that you want to make. It is striking, original or surprising in some way. And whenever you make such a statement, inversion is necessary. So, it has to be:

• 'Only at night do bats leave their cave.'
• 'Only after I had returned home did I realize that I had left my watch in Emma's bathroom.'

 Inversion is also used after the not only ... but also construction:

• 'Not only did we visit Cuba's capital, Havana, (but) we also spent three days exploring the Galapagos Islands off the coast of Ecuador.'

Inversion is also found in expressions containing the word 'no', when placed at the beginning of the sentence:

• 'Under no circumstances are you (allowed) to walk home from school alone.'
• 'In no way will I agree to sharing an office with Ben.

 The same rule operates for 'seldom', 'hardly', 'scarcely', 'rarely', 'never', 'never before' and 'no sooner':

• 'No sooner had I arrived at the station than the train came in.'
• 'Rarely do we see such brightly-coloured birds.'
• 'Seldom do we walk on such green grass.'
• 'Scarcely had we finished lunch when the bell rang for afternoon classes.'

Remember, you are registering surprise, or something similar, when you do this. If it is inappropriate to be so emphatic, you would say:

• 'We had scarcely finished lunch when the bell rang for afternoon classes.'

Inversion after negative expressions, so, and in conditionals?

 I'm getting ready for the TOEFL exam and this part of the website has been really useful for me. I need an explanation for all kinds of inversion and I want to know if it is an obligation to use inversion patterns.

Martine Talbourdet from France writes:

I would like to know if you really use expressions like So do I, So can I, So must I. Do you use them or are they formal?