I
verb
BAD : It doesn't matter the nationality of the archaeologists.
GOOD : The nationality of the archaeologists doesn't matter.
BAD : Doesn't matter the time.
GOOD : The time doesn't matter.
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it doesn't matter + clause: 'It doesn't matter if you can't answer all the questions. Just do your best.' subject + doesn't matter : 'The results don't matter. Just do your best.'
II
noun
1
BAD : No matter he tries hard, he never succeeds in passing.
GOOD : No matter how hard he tries, he never succeeds in passing.
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no matter how/who/whether etc + subject + verb : 'No matter how much you help him, he never seems grateful.' 'No matter how late you set off, the roads are always busy.' 'No matter who you ask, they all say the same thing.'
2
BAD : The matter is that we won't have enough room in the car to take your mother with us.
GOOD : The problem is that we won't have enough room in the car to take your mother with us.
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Matter is used to mean 'problem' or 'trouble' only in questions and negative sentences: 'What's the matter?' 'Is anything the matter?' 'There's nothing the matter.'
3
BAD : After the sauna they run and jump in the river, no matter if it's freezing or not.
GOOD : After the sauna they run and jump in the river, no matter whether it's freezing or not.
BAD : No matter they are rich or poor, they all come to us for advice.
GOOD : No matter whether they are rich or poor, they all come to us for advice.
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no matter + wh- word (NOT if /nothing): 'I'm not interested in the job, no matter how much they offer me.' 'No matter what you do for her, she's never grateful.'
Note that no matter whether tends to sound awkward and there are usually simpler alternatives: 'After the sauna they run and jump in the river, whether it's freezing or not.' 'Rich or poor, they all come to us for advice.'
4
BAD : No matter the recession, sales remained high.
GOOD : In spite of the recession, sales remained high.
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No matter is always followed by a wh- clause: 'No matter what they did, they couldn't put the fire out.' 'No matter how cold it gets, we'll keep warm somehow.'
In front of a noun phrase, use in spite of/despite : 'In spite of the temperature outside, we managed to keep warm.'
5
BAD : The flight attendant told us that there wasn't any matter; it was just a storm.
GOOD : The flight attendant told us that nothing was the matter; it was just a storm.
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nothing/something is the matter or there is nothing/something the matter : 'I think there's something the matter with the central heating. It's cold in here.' 'Don't worry. Nothing's the matter. It's just a tiny cut.'
6
See FACT 3 (↑ fact )
7
See NO MATTER