• Create a mapping from colum/row name to number. A hash can be very helpful here.
• Create an emtpy array or arrays
• For each pair that you read, split it into two names, and use the mapping from the first step to turn it into two column/row numbers. Use that to access the array of arrays, and set the value to 1
• Print the result

TIMTOWTDI, with a HoH... to get you started... though you might get problems with extremely large numbers of Ax;Ay relationships. Then, try to use bitmaps or a DB.
HTH

use strict;
use warnings;

my %A;
my ($max_row, $max_col) = (4,4);

# autovivify interesting rows/cols of %A
while (<DATA>) {
  warn("Line $.: cannot understand: $_") , next unless /A(\d+);A(\d+)/
+;
  my ($row, $col) = ($1,$2);
  $A{$row}{$col}++;
  $A{$col}{$row}++; # uncomment if relationship is not bidirectional
}

# print col. header
print "    ";
printf("A%-3d",$_) for (1..$max_col);
print "\n";

#print matrix A
for my $row (1 .. $max_row) {
  printf("A%-3d", $row);

  for my $col (1 .. $max_col) {
    printf(" %-3d",  exists $A{$row}{$col} ? "1" : "0" );
  }
  print "\n";
}


__DATA__
A1;A4
A2;A3
A2;A4
A1;A3
[download]

    A1  A2  A3  A4
A1   0   0   1   1
A2   0   0   1   1
A3   1   1   0   0
A4   1   1   0   0
[download]

• create an array to define output order, e.g. my @order = sort keys %A; / assumption: symmetric matrix
• replace the (1 .. $max_...) parts by (@order)
• update the printf(...) lines to cope with wider output and string- instead of int-type where necessary

Thanks vey much

If u have horse instead of A1 
          lion instead of A2
          mule instead of A3
          tiger instead of A4
[download]

 
__DATA__
horse;tiger
lion;mule
lion;tiger
horse;mule
[download]

Then in respone to that code tried to modify.

use strict;
use warnings;

my %A;
my ($max_row, $max_col) = (4,4);

# autovivify interesting rows/cols of %A
while (<DATA>) {
  warn("Line $.: cannot understand: $_") , next unless /(\w+);(\w+)/
+;
  my ($row, $col) = ($1,$2);
  $A{$row}{$col}++;
  $A{$col}{$row}++; # uncomment if relationship is not bidirectional
}

# print col. header
print "    ";
printf("%-3d",$_) for (1..$max_col);
print "\n";

#print matrix A
for my $row (1 .. $max_row) {
  printf("%-3d", $row);

  for my $col (1 .. $max_col) {
    printf(" %-3d",  exists $A{$row}{$col} ? "1" : "0" );
  }
  print "\n";
}
[download]

printing as 
    1  2  3  4  
1   0   0   0   0   
2   0   0   0   0    
3   0   0   0   0    
4   0   0   0   0
[download]

output shud be like

  
      horse lion mule tiger
horse  0     0    1    1
lion   0     0    1    1
mule   1     1    0    0
tiger  1     1    0    0
[download]

Thanks

I have tried using that as per suggestions by Perlbotics /p>

#use strict;
use warnings;

my %A = (horse=> 'a',lion=>'b' ,mule=>'c',tiger =>'d');
my @order= sort  keys %A;

while (<DATA>) {
  warn("Line $.: cannot understand: $_") , next unless /(\w+);(\w+)/;
  my ($row, $col) = ($1,$2);
 $A {$row}{$col}++;
  $A{$col}{$row}++;
}

# print col. header
print "    ";
printf(" %2s",$_) for (@order);
print "\n";

#print matrix A
for my $row (@order) {
  printf(" %2s", $row);

  for my $col (@order) {
    printf(" %3d",  exists $A{$row}{$col} ? "1" : "0" );
  }
  print "\n";
}


__DATA__
horse;tiger
lion;mule
lion;tiger
horse;mule
[download]

I have got ouput 
        horse lion mule tiger
 horse   0   0   1   1
 lion   0   0   1   1
 mule   1   1   0   0
 tiger   1   1   0   0
[download]

However If u see in the code i have not use strict command; if using strict command in the first line error displayed will be Can't use string ("a") as a HASH ref while "strict refs" in use at work_matrix.pl line 12, <DATA> line 1.
What can be possible solution if using strict command?