Can't it be ach is iad?
No — a copular statement needs a predicate.
But what if the question was "is he a dog? Yes he is!"
Wouldn't it translate to something like:
An é madra? Is é.
An answer to a yes/no question in that form has an implied predicate (madra in your example).
I see so "is iad" is more like "they are (it)" or "they are (that thing)".
Thanks for the clarification :)
Yes. In fact, that is better than the answer given.
What is the grammatical reason for using tá here rather than bhfuil?
There is no preverb, so the verb is not in the dependent form.