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my @sorted_matrix = sort { natural_cmp($a->[0], $b->[0]) } @matrix;

...
  my ($x,$y) = map { my $key = $_; $key =~ s[(\d+)][ pack "N", $1 ]ge;
+ $key } @_;
  $x cmp $y;
}

0 0 -> A1a1
1 0 -> A1a12
2 0 -> A10a1
3 0 -> A12a1