No matter = (1) in spite of everything; regardless or irrespective of: ‘No matter how hard he tries, he never succeeds.’ (2) it does not matter; it makes no difference: ‘No matter who you ask, they all will say the same thing.’
No matter how/who/whether etc.+ subject+ verb: ‘No matter how much you help him, he never seems grateful.’
No matter+ wh-word (not if/nothing): ‘I am not interested in the job, no matter how much they offer me.’
No matter is always followed by wh-clause: ‘No matter how cold it gets, we will keep warm somehow.’ In front of a noun phrase, use in spite of/despite: ‘In spite of/despite the low temperature outside, we managed to keep warm.’