Here are some examples of how to use it:
* "As a matter of fact, I've been to Paris twice." (Used to correct a previous statement or provide additional information)
* "As a matter of fact, the meeting is tomorrow, not today." (Used to clarify a fact)
* "As a matter of fact, I think you're right." (Used to agree with someone)
So, while "as a matter of fact" is not a single word, it is a correct and common phrase in the English language.