my @PP = ("foo", "bar", "baz");
my @OO = ("AAA", "bar", "CCC");

$PP[1][0] = "foobar";
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#!/usr/bin/perl -l

my @PP = ("foo", "bar", "baz");
my @OO = ("AAA", "bar", "CCC");

$PP[1][0] = "foobar";

print "\@PP: " . join(", ", @PP);
print "\@OO: " . join(", ", @OO);
print "\@bar: " . join(", ", @::bar);
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@PP: foo, bar, baz
@OO: AAA, bar, CCC
@bar: foobar

With use strict; you get the error: Can't use string ("bar") as an ARRAY ref while "strict refs" in use

FWIW, assigning the numbers to the arrays in separate lines makes no difference.

This is because your code's comments are wrong:

# fill two 25 x 25 arrays with zeros, then modify a couple of cells
my @PP = my @OO = (1..25);
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This does not create 25x25 arrays, this creates 1x25 arrays.

Below shows a 1x25 (what you have) vs a 2x5:

use strict;
use warnings;
use Data::Dump;

my @one_by_twentyfive = (1..25); 
my @two_by_five = ([1..5],[1..5]); 
dd \@one_by_twentyfive; 
dd \@two_by_five;
__END__
[1 .. 25]
[[1 .. 5], [1 .. 5]]
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or this one populates a 25x25 array, then overrides 3 slots:

Hello,

you can also initialize an ArrayOfArrays setting default values using x (repetition operator in list context) like in:  @aoa = ([( 1 ) x 3]) x 3

L*

PS I evidently need more coffeine this morning.. see below

There are no rules, there are no thumbs..
Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.

short answer

print this on a t-shirt:

• "use strict or die!"

long answer

$PP[1][2]=3 is a shorter notation for $PP[1]->[2] = 3

so with

$PP[1] == $OO[1] == 1

what you are effectively doing is

1->[2] = 3

which is just populating @1

debugger-demo perl -de0

  DB<46> 1->[2] = 3

  DB<47> x @1
0  undef
1  undef
2  3
  DB<48>
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For good reasons that's forbidden under strict

  DB<45> use strict; my @PP; $PP[1]=1; $PP[1][2] = 3
Can't use string ("1") as an ARRAY ref while "strict refs" in use at (
+eval 66) ...
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> FWIW, assigning the numbers to the arrays in separate lines makes no difference.

Well I hope it's now clearer why...