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Adjectives describe a noun which is marked by が.
僕は料理が得意。
Could it be rewritten as
僕には料理が得意。
Or is it wrong?
Regarding adjectives, a sentence like this would be correct:
僕にはペンが必要です。
Would a sentence like the following one be correct?
僕がペンを必要する。
(I think I should say 必要にする, but I am not sure.)
僕には料理が得意。
is simply ungrammatical.
僕にはペンが必要です。
is grammatical only because 必要だ can take two arguments (AがBに) as word-specific feature, not that it's a universal grammar for adjectives. It's like the English word worth can have an object but most other adjectives can't.
Other adjectives that take に include ふさわしい (あなたが隊長にふさわしい) and 夢中だ (僕は君に夢中だ) etc., but basically you have to learn one by one.
And as already pointed out in comments above:
× 僕がペンを必要する。
僕がペンを必要にする。 → I make the pens necessary.
僕がペンを必要とする。 → I necessitate a pen.
na-adjective + にする results in a verb "make ... adjective" and とする "regard ... adjective".
僕には料理が得意
when you say like this, it will give the impression that someone else you are going to talk about is not good at cook.
It's same like this,
僕にはできません I can't do it (but someone can do it)
僕がペンを大切にする can be translated as I care about the pen.
