The below regex will match the strings that start and end with an alpha character.

/^[a-z].*[a-z]$/igm

The a string also starts and ends with an alpha character, right? Then you have to use the below regex.

/^[a-z](.*[a-z])?$/igm

DEMO

Explanation:

^             #  Represents beginning of a line

[a-z]         #  Alphabetic character

.*            #  Any character 0 or more times

[a-z]         #  Alphabetic character

$             #  End of a line

i             #  Case-insensitive match

g             #  Global

m             #  Multiline