Yes, it's wrong. And there is no form "dużę".
In a sentence built as "X is Y", Instrumental is used when Y is a noun phrase, but if Y is just an adjective (as here), it stays in Nominative.
So you are right that if the sentence was "That fish is a big animal", that would take Instrumental (Tamta ryba jest dużym zwierzęciem).
You may read more about it here: https://www.duolingo.com/comment/16373167
Would it be correct to translate "My big fish" to "Moja duza ryba"? Or for example would "My big brother" be "Moj duza brat"? Sorry for missing out the accents. I'm just wondering because google translate changes "duza" to "wielka" and "starszy" respectively and I wasn't sure why. What I mean is it translates:
"My big fish" to "Moja wielka ryba" and "My big brother" to "Moj starszy brat". I don't understand why that is and wanted to ask if someone could explain why?
Adjectives „duży” and „wielki” mean "big" and "great". You can say „moja duża ryba” or „moja wielka ryba” without issue. It all depends with what you wanted.
„Starszy” means "older". In Polish we simply don't say "big brother", but "older brother" (unless you meant literally big in size, then „duży brat” would be appropriate). Or when you refer to the big brother that sees everuthing (like from Orwell's novel or reality TV show), we call him „wielki brat” (great brother).
I think it's because using the Instrumental after the verb "być" would be equating to the subject. Since an adjective can't be equal to the subject (it can only describe it), it isn't used in the instrumental case.
It is easy to see why it is like this with examples;
Pies nie jest kotem - Two nouns are being equated here, so 'kot' must be in the instrumental case (ignore the negation (nie)... whether a sentence is negated or not, the second noun after być will always be in the Instrumental case)
Twój pies jest czarny - Here, we are just describing the dog, so it's in the Nominative case
To make it easier, just remember these two things;
Noun+być+noun - second noun in Instrumental
Noun+być+adjective - adjective in Nominative