Something that is literally or factually true, as in The records showed it to be a matter of fact that they were married in 1960. This idiom often occurs in the phrase as a matter of fact, as in As a matter of fact, you are absolutely right. Matter of fact was first recorded in 1581, and originally was a legal term distinguishing the facts of a case from the law, called matter of law, applying to it. It began to be applied to other concerns in the late 1600s.
American Heritage Idioms