The verb enter is a transitive verb when referring to physical movement into a place; therefore, no preposition is required after it.

১. Using ‘entered into’ is a common error; it is only used figuratively (e.g., entered into an agreement).
২. For physical locations like a room or building, we say “entered the room” directly.
৩. ‘In’ and ‘to’ are redundant because the meaning of entry is already contained within the verb.

অতিরিক্ত তথ্য: Similarly, verbs like ‘reach’ and ‘discuss’ often do not take prepositions.