“Both/both of” as predeterminer
Incorrect : Her parents are both doctors.
Correct: Both her parents are doctors. Or Both of her parents are doctors.
Note: You can use both or both of before nouns with a determiner. But "both of” cannot be used before nouns without a determiner. For example:
Incorrect: I like both of paintings.
Correct : I like both of the paintings. Or I like both paintings.
"Both of” can be used before personal pronouns. For example:
Both of them can speak English.
I like both of you to come.
"Both" can be used after the pronoun with the same meaning. For example:
They both can speak English.
I like you both to come.
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