A little off-topic, but you should be aware that $a and $b are special variables associated with sort. It's generally considered risky/poor-form to use them outside of that context. Just to help you avoid developing bad habits.

To answer your original question, you could modify your posted code to get

while (@AoA) {
    my $var = shift @AoA;
    my $a = $var->[1];
    my $b = $var->[2];
}
[download]

or

while (@AoA) {
    my $var = shift @AoA;
    my ($a, $b) = @{$var}[1,2];
}
[download]

or

while (@AoA) {
    my @var = @{shift @AoA};
    my $a = $var[1];
    my $b = $var[2];
}
[download]

or

for my $i (0 .. $#AoA) {
    my $a = $AoA[$i][1];
    my $b = $AoA[$i][2];
}
[download]

or...