The 1st pattern A Major scale uses the C shape open chord. When looking at the open C chord, the root notes are on the 1st fret B string and the 3rd fret A string.
C
Important: The notes used in the A Major scale are A B C# D E F# G#, there are three sharps in the A Major scale.
If we take a look at the scale on the fretboard, you will see something like the following pattern… the root notes are marked with the “X“
| $1.9.$2.9.$3.9.$4.9.$5.9.$6.9 | $1.10.$2.X.$6.10 | $3.11.$4.11.$5.11 | $1.12.$2.12.$4.12.$5.X.$6.12 |
Note: In the diagram above it’s the fret numbers that are indicated not the scale degrees, and it isn’t the way you would normally write out a scale using TAB, it’s just to illustrate the fingering pattern of the scale. 
When playing this scale on the guitar, I normally start on the lowest pitch root note, which is at the 12th fret on the A string, and play up to the highest pitch note of the scale, 1st string 12th fret, which is an E note.
| $5.12 $4.9 11 12 $3.9 11 $2.9 10 12 $1.9 10 12 |
Descending back to the lowest pitch note of the scale, the C# on the 9th fret Bottom E string.
| $1.12 10 9 $2.12 10 9 $3.11 9 $4.12 11 9 $5.12 11 9 $6.12 10 9 |
Then back up in pitch to the A root note on the 12th fret A string.
| $6.9 10 12 $5.9 11 12 |