To create a chord from a scale you use the 1st, 3rd, and 5th of the scale, these three notes become the A Major Triad or A Major Chord.

Adding these to notes to the scale tones is called harmonizing. The notes added for the A triad is C# and E, the C in the A Major scale is sharp notice the Key Signature three sharps equals the Key of A.

These three notes are made from the 1st, 3rd, and 5th notes, but the first note is always the note you start on. For the A triad, the A, C# and E are the 1st, 3rd and 5th with the A being the 1st note. For the B triad is will be B,D,F with the B being the first note. So creating a Major chord has the formula of 1-3-5.

By creating chords in this matter for the A Major Scale the chords you end up with are A Maj, B Minor, C# minor (C#m), D, E, F#, G# diminished then back to A.

The chords created are also called Diatonic chords since they are specific chords for the A Major scale.

If you play a chord progression of I, IV, V in the Key of A the chords would be A, D and E.

The next note we can add for harmonizing is the 7th note of the root, depending on this 7th note the chord then becomes either a Major 7th (such as Amaj7), Minor 7th (such as Bm7), or a Dominiant 7th (G7).

Let me explain why the B in A Major is a B minor. When you build Major chords you always use the Major scale of the chords you building so for the B major chord the B Major scale is used and the B Major scale contains the sharps F,C,G,D,A. Remember take the last sharp and raise to the next note to find the Key Signature. If we use the 1-3-5 of the B scale the notes are B, D#, F# but when we use the A Major scale and harmonize the notes we don't have the D# any longer and the chord changes. The formula for the B chord we build in the A Major scale is 1,b3,5 where the 3rd is flat a 1/2 step and this is the formula for a Minor chord. This is why some chords are sharp, minor and diminished.