/^[a]*$/ matches a string containing 0 or more 'a' characters which may be followed by a new line character.

Note that the character class is redundant. It could equally well be written /^a*$/.

Consider:

use strict;
use warnings;

my @strings = ('', '1', 'a', "a\n");
/^[a]*$/ && print "/^[a]*\$/ matches >$_<\n" for @strings;
/^a*$/ && print "/^a*\$/ matches >$_<\n" for @strings;
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Prints:

/^[a]*$/ matches ><
/^[a]*$/ matches >a<
/^[a]*$/ matches >a
<
/^a*$/ matches ><
/^a*$/ matches >a<
/^a*$/ matches >a
<
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