The opposite of 'opinion' is 'fact'. However, the opposite of a noun is not well-defined - what's the opposite of 'car'. It would make more sense to ask what is the opposite of the adjective 'opinionated', which is 'open-minded'.

The opposite of an opinion is not a fact. An opinion is an idea or belief that is not or cannot be proven. ex: Strawberry ice cream is better than vanilla ice cream. A fact is a proven idea. ex: 2+2=4 A opinion can become a fact. ex: People used to believe that the world was flat. At that time there were also people who believed that the world was round. The opinion that the world was round became a fact when it was proven. The opposite of "opinionated" is not open-minded it is "indifferent". The opposite of "open-minded" is "close-mined". To be opinionated means to have opinions. To be "indifferent" is to not have an opinion. "Open-minded" is to be open to ideas and "close-minded" is to not be open to ideas. The closest words I could think of to being the opposite of the word opinion would be either the word indifference or the word apathy.

The opposite of opinion is "intelligence".