The following echoes Eily's suggestion:

use strict;
use warnings;

my @AoA;

while (<DATA>) {
    chomp;
    push @AoA, [ split '' ];
}

for my $i ( 0 .. @AoA - 1 ) {
    for my $j ( 0 .. @{ $AoA[0] } - 1 ) {
        print "String $i; Char $j: '$AoA[$i]->[$j]'\n"
    }
    print "\n";
}

__DATA__
String 1.
Another 2
abcdefghi
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Output:

String 0; Char 0: 'S'
String 0; Char 1: 't'
String 0; Char 2: 'r'
String 0; Char 3: 'i'
String 0; Char 4: 'n'
String 0; Char 5: 'g'
String 0; Char 6: ' '
String 0; Char 7: '1'
String 0; Char 8: '.'

String 1; Char 0: 'A'
String 1; Char 1: 'n'
String 1; Char 2: 'o'
String 1; Char 3: 't'
String 1; Char 4: 'h'
String 1; Char 5: 'e'
String 1; Char 6: 'r'
String 1; Char 7: ' '
String 1; Char 8: '2'

String 2; Char 0: 'a'
String 2; Char 1: 'b'
String 2; Char 2: 'c'
String 2; Char 3: 'd'
String 2; Char 4: 'e'
String 2; Char 5: 'f'
String 2; Char 6: 'g'
String 2; Char 7: 'h'
String 2; Char 8: 'i'
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$AoA[$i]->[$j] explained:

$AoA[$i]->[$j]
      ^  ^  ^
      |  |  |
      |  |  + - Character number in string
      |  + - Dereferencing arrow
      + - String number in array
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The above builds an array of arrays (AoA) by splitting each string on an empty string to create a list of the string's characters in an anonymous array whose reference is pushed onto @AoA. The nested loops iterate through the AoA, using the dereferencing arrow -> to access each character. The notation @{ $AoA[0] } - 1 was used to obtain the number of characters in the dereferenced array (effectively the string length), since you mentioned that each string had the same length.

Hope this helps!