I have an example of Powerset construction from the lecture.
Powerset construction is applied on automata A1. The result is automata A2. You could see I do Powerset construction myself below the A1 and A2. I didn't get a state {2} in the result. Could anyone point out where I was wrong?
Actually both answers are correct. In the first answer, the full powerset automaton is computed. That is, for every subset $S$ of the set of states, and for each letter $a$ of the alphabet, $S \cdot a$ is computed.
In your solution (and this is usually what is done), you are just interested in the states reachable from the initial state. And as you can see, the state $\{2\}$ is not reachable. This is why you don't have it in your construction.