As a matter of fact
The little word, fact, offers itself for endless variations of usage. As a matter of fact or in fact is used to add emphasis to what you are saying, or to show that it is the opposite of or different from what went before. No I don’t work. In fact, I’ve never had a job.
“Have you always lived here?” “As a matter of fact (= the truth is) I’ve only lived here for the last three years.” So do not use in fact or as a matter of fact in general or introductory statements. “In the last two decades advances in technology have in fact changed the face of industry” is wrong.
To correct what someone thinks or supposes, use in fact, as a matter of fact or actually: “He’s a friend of yours, isn’t he?” “No, he is isn’t. As a matter of fact, I’ve just met him.” People think they’ve got lots of money, but in fact the Chatterjees are quite poor. “I’m sorry to have kept you waiting.” “Well, actually I’ve only just arrived.”
Use the fact is that to introduce your main point, especially when this explains the real truth about a particular situation: “I’m not surprised that he’s looking worried. The fact is that he’s been spending more than he earns.” “We don’t really want to go, but the fact is that we don’t have any choice.” Do not drop the that in this usage.
The adjectival phrase matter-of-fact, usually hyphenated, means “not showing feelings or emotion, especially in a situation when emotion would be expected”. He spoke in a very matter-of-fact way about the accident. You can also be adventurous and use the adverbial form, matter-of-factly, or the noun, matter-of-factness.
A fact of life is something unpleasant that cannot be avoided. Going bald is just a fact of life. But make it plural, and the phrase, facts of life, means the biological, and usually reproductive, facts of sex - the birds and the bees. Facts and figures refer to exact detailed information. We’re getting some facts and figures together, and we will then have a full board meeting.
The preposition that goes with the most common use of fact is about. I don’t know all the facts about the case. Do not use clumsy constructions like due to the fact that for because, or in spite of the fact that for although.
Something more
Let alone and much less are two expressions which are sometimes used backward. When you write not X, let alone Y or not X, much less Y, then Y must be something more ambitious, more difficult or more spectacular than X. It is all right to write: He can’t ask for a glass of water in Hindi, let alone converse in the language, but it is wrong to write: He can’t converse in Hindi, let alone ask for a glass of water in the language. The phrases, let alone and much less, do not mean “not even”.