Like this? :)

#! perl -slw
use strict;

my @AoA = (
   [ '1', '2', '10' ],
   [ '3', '4', '5'  ],
   [ '6', '8', '11'  ],
   [ '0', '7',  '9'  ],
);

my @A = qw(0 0 0 0 1 2 0 0 1 0 1 0);

my( $i, $j ) = ( 0, 0 );

$j++ < $#{ $AoA[ $i ] } or $i++, $j=0
    while $i < @AoA and not $A[ $AoA[$i][$j] ];

## Updated per [ysth]'s observation below
print $i == @AoA ? 'not found' : "i:$i j:$j"; 


__END__
C:\test>junk
i:0 j:2
[download]

How about a deobfuscated version?

Not very satisfying because of the need to use a 'goto' to quit the loops early, and the need to duplicate the index vars because Perl localises them to loop even if they are pre-existing vars.

I tried suggesting that the latter behaviour was a bug a while ago and got shouted down.

#! perl -slw
use strict;

my @AoA = (
   [ '1', '2', '11' ],
   [ '3', '3', '6'  ],
   [ '6', '8', '11'  ],
   [ '0', '7',  '9'  ],
);

my @A = qw(0 0 0 0 1 2 0 0 1 0 1 0);

my( $p, $q );
OUTER: for my $i ( 0 .. $#AoA ) {
    for my $j ( 0 .. $#{ $AoA[ $i ] } ) {
        ( $p, $q ) = ( $i, $j ) and last OUTER
            if $A[ $AoA[ $i ][ $j ] ];
    }
}
print "i:$p j:$q";
[download]

I'm not sure why you are using the outer loop below?

---

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

# look for @AoA row and col containing index
# for first non-zero element in @A
for my $index (0..$#A) {
   if ($A[$index]) {
      ROW:
      for my $row (0..$#AoA) {
         for my $col (0..$#{$AoA[$row]}) {
            if ($AoA[$row][$col] == $index) {
               print "$row $col\n";
               last ROW;
            }
         }
      }

      last;
   }
}
[download]