A good practice is to have
use strict;
use warnings;
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++;
}
or
my $i;
my $j;
while <$input>{
$j = (/^[A-Z]) ? 0 : $j+1;
$AA[$i++][$j] = $_;
}
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