I'm working on the modes now...kinda getting it, kinda not. I'm not getting the "math" on it. Let's say a E mixolydian is an A major with the root shifted to E.
A major is A - B - C# - D - E - F# - G# - A
E major is E - F# - G# - A - B - C# - D# - E
The mixolydian mode has a flat 7. So we flatten the 7 of E major to D and now we have:
E - F# - G# - A - B - C# - D - E and when shifted to A as the root we have
A - B - C# - D - E - F# - G# -A.............same as
A - B - C# - D - E - F# - G# - A ( A Major)....correct?
You're not quite right there. What you need to understand is that if you're playing in A major and the mode you're playing is E Mixolydian, you're not playing with E as the root, you're starting the scale on the 5th degree. This is very important to visualise as it will instantly make sense of why the notes are all the same.
Now, onto your question. By flattening the 7th of E major you are turning that mode from Ionian into Mixolydian, which means that the Ionian mode of that scale (AKA the "root note" mode) is B. This means that the mode starting on A is Locrian, which gives you the following notes:
A - Bb - C - D - Eb - F - G - A
The scale which that mode belongs to is then termed "B major".
EDIT: reading your post again, it looks like your confusion has caused some ambiguity. Basically, you've taken the A major scale and moved the root to the E (the Mixolydian mode), AKA the 5th degree. You've then asked that if you move the root back to A, would it be the A major scale again (starting on the root degree of the scale, AKA the Ionian mode). The short answer is yes. My initial response was assuming that you were changing E mode from Ionian to Mixolydian, which it seemed like you were.
In the same way, I can say that B Aeolian is a D major with root note shifted to B.
So B major scale is B - C# - D# - E - F# - G# - A# - B
Aeolian has a b3-b6-b7... D G A
And we're left with B-C#-D-E-F#-G-A-B (Which is a D major with the rote shifted to B)
So the easy way to do this is to just move the root note and keep the scale notes as is, but to understand, we have to know what the differences between notes is (ie, what is flattened and what is sharpened).
Yes?
Now you're talking, THAT is correct. Modes are about taking the same notes in the same scale, and just starting from a different note (i.e. using a different note as the root). This results in different intervals which basically just have to be learned raw in order for you to be familiar with the modes in full. You seem like you're onto that though which is good. Top Tip: learn the characteristic intervals for each mode to be able to use them in a compositional scenario better.
Again, learn that the natural minor scale simply starts on Aeolian instead of Ionian. Makes working through minor scales just as easy as Major, and allows you to quickly recall relative major/minor scales rather than just parallel scales ("relative" meaning same notes but different root, "parallel" meaning different notes but same root).
Next, I recommend you learn the circle of fifths to easily recall how many sharps/flats there are in each scale, and learn piano keys to easily visualise what those sharps and flats actually are.