> How do I correctly set up and reference this array?

If I was you I'd rather use an array reference. There is no need to do this, but it feels more appropriate. Your array could look like this:

my $array_ref =
[
    [ 123, 456 ],
    [ 234, 567 ],
    [ 345, 678 ]
];
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This array reference can be used in a variety of ways, but the most obvious are these:

my $pos = $array_ref->[$x][$y];

my $row = $array_ref->[$x];
my $column = $row->[$y];
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Regards,
-octo