The time line in your resume must be complete. For instance (not yours), if there's a gap, have a reason for it, and be ready to explain why it was, and what you did while you were idle. "Tutored kids on spreadsheets at the Library", or something.
In the US, with the privacy laws being what they are, one of the few things a company can ask a former employer, and one of the few things they can answer, is your dates of employment. Dates on a resume are easily and usually verified. If there's a problem (Company A), you can survive if you're honest. If someone discovers a problem without your admitting it up front, your resume won't even hit the edge on it's way to the circular file.
Everybody stumbles sometime. Myself, many times. I used to ask potential vendors for 6 references. 3 where thing went well, and 3 where they didn't. I wanted to know how they reacted when an installation wasn't going well. If they were honest, and capable, I got all 6 references. If I didn't get all 6, they didn't sell to me. I'd suggest you do the same. If you had a problem with Company A, explain it; explain what you learned from the experience, and why you're now better for the experience. People respect honesty, it's not that common.
Keep at it, you'll find a place to shine. Best of luck to you.