You’re right that AI isn't perfect, but it’s pretty good. Especially since December last year which was an inflection point in capability.
Of course they can. Even older models can. They do better at this when given permission to say so, just like a very anxious student facing a maths exam question may need to be reminded "find the exact square root of 2 in the form a/b, or prove this isn't possible".
https://chatgpt.com/share/69ef0785-f290-8328-b6fa-3207be2c0b...
The easy part of spotting an LLM is how few people ever change the default settings; my personalisation includes telling it to say so when unsure or that it doesn't know, along with some of the other weaknesses of LLMs.
There are other patterns in LLMs, but the better the tools are wielded the harder it is to spot them.