Explanation:

Introduction:
- An epsilon transition is a transition in a Non-Deterministic Finite Automaton (NFA) where the machine can move from one state to another without consuming any input symbol.
- Eliminating epsilon transitions from an NFA involves removing these transitions and updating the transitions to ensure that the language recognized by the modified NFA remains the same.

Preservation of Language:
- When eliminating epsilon transitions from an NFA, the goal is to transform it into an equivalent NFA without epsilon transitions.
- The process involves creating new transitions and updating existing transitions to account for the elimination of epsilon transitions.
- The language recognized by an NFA is defined by the set of all possible strings that can lead the machine from the initial state to any accepting state.
- The process of eliminating epsilon transitions preserves this language, i.e., the modified NFA still recognizes the same set of strings.

Steps for Eliminating Epsilon Transitions:
1. Closure: Identify all states that can be reached from a given state using epsilon transitions. This set of states is called the epsilon closure of the given state.
2. Removal: For each state in the NFA, remove all epsilon transitions and update the transitions accordingly.
- Any transition that goes through an epsilon transition is replaced by a combination of transitions that skip the epsilon transition.
- For example, if there is a transition from state A to state C via epsilon, and a transition from state C to state B via 'a', then a new transition is added from state A to state B via 'a', bypassing the epsilon transition.
3. Repeat: Repeat steps 1 and 2 until no more epsilon transitions exist in the NFA.

Preservation of Language:
- The process of eliminating epsilon transitions does not change the language recognized by the NFA.
- By updating the transitions and removing the epsilon transitions, the modified NFA still accepts the same set of strings as the original NFA.
- The closure operation ensures that all paths that were previously possible through epsilon transitions are still valid after the elimination process.
- Therefore, the language recognized by the NFA is preserved throughout the elimination of epsilon transitions.

Conclusion:
- The language recognized by an NFA is preserved throughout the process of eliminating epsilon transitions.
- The steps involved in the elimination process ensure that the modified NFA still accepts the same set of strings as the original NFA.
- Therefore, the correct answer is option 'A' - yes.