Thank you to KeĆr Finlow-Bates for sharing his videos.
"The other week I was asked by someone if a smart contract could sign a challenge to prove something, for example ownership of another contract. "
The answer is no, because a smart contract doesn't have a private key.
The person asking the question was quite taken aback by this fact, so I've made this video to explain why, and look at Ethereum addresses in general.