Is it reasonable to consider that an encryption scheme must be invertible? I am in a dispute regarding a test question in an exam.
The question is something like that:

What would happen if one were to use RSA with $n=100$ and $e=13$ to
encrypt a message $m$?
a) You would be able to encrypt the message but not decrypt it.
b) You would not be able to encrypt the message.
...

Both parties agree that the operation $c = m^e \bmod n$ (a transformation known as encryption when using proper RSA) is no longer bijective, as $n$ is not the product of two primes. For example, $m=10$ and $m=20$ would both result in &quot;cryptogram&quot; $c=0$.
I consider that an encryption function must be invertible, as the purpose of encryption is to hide information from non-authorized eyes while allowing authorized parties to retrieve it. The fact that this transformation (which I'd argue could not even be called RSA, as $n$ does not fulfill RSA's rules) is not bijective means that it is not invertible, so it cannot be considered encryption. I would say that, under this assumption, any discussion of encryption/decryption is pointless, and if one answer had to be marked, it should be B: we cannot call $c = m^e \bmod n$ &quot;encryption&quot;.
On the other hand, the other party sustains that the only correct answer is A, and that &quot;it is fallacious to believe that encryption must be invertible, as there are many non-invertible encryption schemes&quot;. They are not available for questioning, so I cannot seek further clarification about what they meant. I assume they meant cryptographic hashes, but I would not consider them encryption schemes, but cryptographic primitives.
My question is therefore two-fold:

Am I correct in assuming that it is not wrong to impose the condition that a transformation must at least be invertible in order to be considered encryption?
If I am correct: Could I be pointed out to some reputable bibliographic source to use to strengthen my case?
If I am incorrect: Is it because cryptographic hashes are considered encryption schemes or because there truly are non-invertible cryptographic schemes? If so, how do they meaningfully differ from hashes?
Am I correct in assuming that it is not wrong to impose the condition that a transformation must at least be invertible in order to be considered encryption?


Yes, strictly speaking: Encryption is the process of turning a plaintext message into a ciphertext (encryption) which then can later be turned back into the original plaintext (decryption).



If I am correct: Could I be pointed out to some reputable bibliographic source to use to strengthen my case?


Gary Kessler has published An Overview of Cryptography.
In chapter 3 &quot;Types of cryptographic algorithms&quot; you can see that there is a distinction drawn between encryption and hash functions.



If I am incorrect: Is it because cryptographic hashes are considered encryption schemes or because there truly are non-invertible cryptographic schemes? If so, how do they meaningfully differ from hashes?


Encryption, decryption and cryptographic hashes all belong together in the realm of cryptography but they can definitely not be used interchangable (see this earlier answer from a different question). Some differences include:
Reversability
Encryption schemes can usually be transformed back into their original form, i.e. a once encrypted plaintext message can usually be decrypted back into the original plaintext. Hashes, on the otherhand, are created in a manner that the input undergoes a loss of information, ultimately making it irreversible.
You can always create a hash from a given input but it's not possible to be sure what the original message once was if you're only given the hash (see pigeonhole principle).
Keys
Encryption schemes always use keys. Hashes do not require keys.
Length
A long plaintext message results in a long encrypted ciphertext &amp; a short plaintext message results in a short encrypted ciphertext.
Hashes will always have a predefined length, no matter the input.