大きじゃない vs 大きくない？

Question

If I understand correctly, only 大きくない can be used?

e.g., 猫は大きくない, not 猫は大きじゃない?

Answer 1

When the adjective 大きい is negated, it becomes 大きくない.

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Although the word 大きな also exists, you can't replace the な on the end with copula forms like で or だ:

　大きな猫　　　　　　 'large cat'

＊大きだ　　　　　←　 ungrammatical
＊大きではない　　←　 ungrammatical
＊大きじゃない　　←　 ungrammatical

This is different from most na-adjectives:

　きれいな花　　　　　'pretty flower'

　きれいだ　　　　←　 grammatical
　きれいではない　←　 grammatical
　きれいじゃない　←　 grammatical 　　　　　　

So even though it ends in な, we have to be careful not to treat this word as a normal na-adjective.

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This word isn't classified as a 形容動詞 (na-adjective) in most monolingual dictionaries. Instead, it's usually classified as a 連体詞 (adnominal word). This is a class of non-inflecting words that appear before nouns, including words like この and とある.

However, Daijirin points out that 連体詞 generally can't function predicatively, while 大きな can:

　耳の大きな人　　←　耳の大きな is a relative clause in which 大きな predicates on 耳

So it may make more sense to classify it as a special kind of 形容動詞 instead, one with a restricted distribution (or set of forms). Either way, though, it's a bit exceptional, so just keep in mind that this word is special and doesn't fit perfectly into any category.

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In this answer, the ＊ symbol means 'ungrammatical.'

Answer 2

Yes. If you say "it is not big", you say "大きくない" in Japanese. 大きじゃない　is wrong. And you can say "大きくはない".