A good practice is to have

use strict;
use warnings;
[download]

at the top of a Perl script. Then you would've seen that you have problems in your use of $j. (It appears to be defined solely in the scope of your initial if, and not defined in the else.)

Other Monks have addressed a better way to solve your problem, but in the case of this specific program, you'd want to say my $j; before the while, and remove the my from the if.

Your code would then look like

my $i=0;
my $j;

while <$input>{
   if (/^[A-Z]){
     $j = 0;
   }
   else {
     $j++;
   }
 
   $AA[$i][$j] = $_;
   $i++;
}
[download]

or

my $i;
my $j;

while <$input>{
   $j = (/^[A-Z]) ? 0 : $j+1;
   $AA[$i++][$j] = $_;
}
[download]