Is "times" really a plural noun?

I think it depends on how you perceive the word. For example, Merriam-Webster defines times as a preposition meaning:

multiplied by: 'three times two is six'

in the same way it defines minus:

[preposition] used to indicate that one number or amount is being subtracted from another

All 5 other dictionaries I can check now, Wiktionary, Collins Online Dictionary, American Heritage Dictionary of the English Language Fifth Edition (2011), Random House Kernerman Webster's College Dictionary © 2010, Dictionary.com define it as a preposition.

If times is classified as a (plural) noun, three times two would be a three-word compound noun where the first and second noun usually function as a noun adjunct which modifies the last noun as in "health care center" or "Obama Byden administration". The role of the noun times in the middle is not very clear.

However, if times is classified as a preposition, times two in "three times two" will be a prepositional phrase which can post-modify the noun three.

Three times two is six. Three minus two is one.
The book on the table is mine. The book under the table is yours.

We can notice that the times/minus two works in the same way as on/under the table as a post-modifying prepositional phrase. Times seems to be closer to a preposition than a noun.

The Oxford Dictionaries define minus as a preposition, which is inconsistent with their definition of times as a noun.

The mathematical operations minus, plus, times have a different syntax than most of English, and this apparently confuses grammarians. None of the traditional parts of speech fits them perfectly, but in my opinion preposition comes closest.