鍵 and 錠: keys and locks
Distinguish a key from a lock and learn the phrase 鍵をかける.
Using a key
鍵, read かぎ, refers to a key used to lock or unlock something. 鍵をかばんから出しました。 says that someone took a key out of a bag.
鍵をなくしました。 reports losing a key. It does not identify anyone who took it or say that the lock is broken.
The locking mechanism
錠, read じょう, here means a lock. 古い錠を取り替えました。 says that someone replaced an old lock.
鍵を錠に差し込みました。 means inserting a key into a lock. Insertion alone does not establish that the door was opened.
An expression for locking
ドアに鍵をかけました。 means locking the door. Do not translate it literally as merely hanging a key on the door.
鍵はありますが、錠が壊れています。 says that the key is available but the lock is broken. Read the states of the two objects separately.
Does 鍵を錠に差し込みました establish that the door opened?
Show the answer and why
No. It reports only that the key was inserted.