Question after the word "after"

[chfkm]

I want to ask about the word "after" .
it's said that a full sentence should follow the word "after". The question is that can I omit the subject of the second sentence if it is the same subject as the first one? For example,

"he started working after he graduated from university"

can I change to

"He started working after graduated from university".

If yes, will it be less formal or the same as before? will that example be the same if I modify it to "after graduating from university."

"Please turn off the machine after use" or "Please turn off the machine after using", which one is correct?

The grammer of that word really confuses me a lot. Thanks for anyone who answers the question.

[Anglika]

I want to ask about the word "after" .
it's said that a full sentence should follow the word "after". The question is that can I omit the subject of the second sentence if it is the same subject as the first one? For example,

"he started working after he graduated from university"

can I change to

"He started working after graduated from university". You can express it "He started work after graduating from university". This is a very usual way of making this statement.

If yes, will it be less formal or the same as before? will that example be the same if I modify it to "after graduating from university."

"Please turn off the machine after use" or "Please turn off the machine after using", which one is correct? Both are correct.

The grammar of that word really confuses me a lot. Thanks for anyone who answers the question.

after = • preposition
1 in the time following (an event or another period of time). [examples as above]
2 behind. The dog walked after the man [the dog was following the man]
3 in pursuit of. The dog ran after the cat [the dog was chasing the cat]
4 next to and following in order or importance. This prize comes after the Nobel prize in value.
5 in allusion or reference to. That saying is after Shakespeare's Hamlet soliloquy.

[chfkm]

Thanks for your answer. It's very comprehensive.

[Anglika]

You're welcome