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#!/usr/bin/perl
my @ar1;
...
$ar1[1][2] = "five";
my $count = scalar @{ $ar1[1] };
print "count = $count\n";

However, if I create the array this way it doesn't work:

...
$ar1 = (["one", "two"], ["three", "four", "five"]);
my $count = scalar @{ $ar1[1] };
print "count = $count\n";