If I have a file claimed to be “encrypted using AES algorighm”, can I verify that their claim is true?
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Only if you have the key. (and IV)
Encryption produces arbitrary byte sequences; most algorithms do not have any characteristics about their output.
In fact, one can design a ciphertext which corresponds to two different plaintexts using two different keys or algorithms.
However, depending on what the file is, it may have a (plaintext) header specifying the encryption algorithm (and that header may be lying).