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Union & Concatenation property of regular language are closed for both DFA & NFA. But while doing union or concatenation of 2 DFAs, we have to insert epsilon transition between both. Adding epsilon doesn't leave DFA as DFA but make them epsilon-NFA. So is both property closed for DFA?

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Actually,
DFA , NFA and epsilon- NFA all are equivalent.
The below image tells that ,
we can convert epsilon- NFA to DFA ,  NFA to DFA. epsilon- NFA to NFA
To concatenate or union two FA , we use  epsilon moves because it is esy using epsilon- NFA.
then you can covert the epsilon- NFA to DFA by applying subset construction method.
So both properties are closed for DFA.
If you have still doubt, you can ask.

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