Storing and accessing stuff in a 2d array can get a little hairy syntactically. Here's some example code:

my $list = [];  # let's start with an array ref
while (<>) {
  chomp;
  push(@$list, [split(' ', $_)]); # note the array ref [] constructor
}
# access the i-j-th element:
print "list[2][3] = ", $list->[2]->[3], "\n";
# access by rows:
for my $i (0..$#$list) {
  print "number of elements in row $i: ", scalar(@{$list->[$i]}), "\n"
+;
  print "last index of row $i = ", $#{$list->[$i]}, "\n";
}
# access each element:
for my $i (0..$#$list) {
  for my $j (0.. $#{$list->[$i]}) {
    print "list[$i][$j] = ", $list->[$i]->[$j], "\n";
  }
}
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If you are doing a lot of matrix operations on your 2D-arrays, you might look into PDL as an alternative.