L1:{<M> | there exist a Turing machine M' such that <M>$\neq$<M'> and L(M) = L(M')}
How this problem becomes trivial? and if it non-trivial then please explain why is that so. According to my understanding, non-trivial properties are the one where a language or string may get accepted by some Turing machine and not by some other Turing machines and hence it becomes undecidable. Hence it becomes undecidable when a given Turing machine it will accept a given string or not as it becomes non-trivial property.
For every non deterministic TM M1 there exists an equivalent deterministic TM M2 recognizing the same language, in this case we will have 2 different machines and both will accept same language, is this description holds true?? and if it is then is it okay to say M1=M2 because they are kind of same machine but other one is just with some non deterministic nature.