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Not in the way you are using it.
"Small is the opposite of big" is saying that the two words mean opposing things. This is okay, because "of" indicates a difference in essence.
"Small is opposite to big", however, indicates an opposition in physical position. It suggests that "X" is in the opposite position compared to "Y". The "to" in this phrase indicates a physical opposition, where the words "small" and "big" do not have physical entities to represent them, and it would only make sense if you were putting the words physically in a list, and saying they were opposite to each other on that list.
If you mean that small is the antonym of big, then (1) is the normal construction. Opposite to is sometimes used for things that face each other, but to is often omitted.
Hi English speakers,
Which of these are gramatically correct and which one do you prefer?
Opposite (physical location):
My home is opposite to the school.
My home is opposite the school.
Opposite (non physical quality):
3. My opinion is opposite to his.
4. My opinion is opposite his.