I look up the examples of "no matter" in some web dictionary and don't find a sentence containing "no matter whether". But in the examples of "whether" and "irrespective" I do see sentences "He's going to buy a house whether he gets married or not." and "He was one of those men to whom a girl's left hand is simply a girl's left hand, irrespective of whether it wears rings on its third finger or not." So is "no matter whether" OK or a redundancy or grammatically wrong? But if it's a redundancy, doesn't "irrespective of whether" (in the aforementioned sentence) sound like a redundancy, too (because using "whether" suffices to convey the idea) ? Should I just use "no matter" or "whether", instead of "no matter whether", in sentences of this type? Or either way is OK?
For example, is saying "The conclusion holds true no matter whether the proof is carried out through this formulation or that formulation." a redundancy or grammatically wrong? Should I just say "The conclusion holds true whether the proof is carried out through this formulation or that formulation." or "The conclusion holds true no matter the proof is carried out through this formulation or that formulation."? Or either of the three ways is OK?