Searching array of arrays in perl

Suppose there are two arrays of arrays:

@A = ( [A, 1], [B, 3], [C, 4], [D, 6] );
@B = ( [A, 2], [B, 5], [C, 3], [A, 3], [E, 7] );

For each of $A[0][0], $A[1][0], $A[2][0]..., I want to find the corresponding one in @B (match the letter, like $A[1][0] eq $B[1][0]), and print out both the second item, for example, $A[1][1] and $B[1][1].

How can I do this in perl? grep + map? Hope I clarify the problem here.

Thanks a lot!

@A = ( [A, 1], [B, 3], [C, 4], [D, 6] );
@B = ( [A, 2], [B, 5], [C, 3], [A, 3], [E, 7] );
push @arr,@{$_} foreach(@A);
push @brr,@{$_} foreach(@B);
for($i=0;$i<=$#arr-1;$i+=2){
        if($brr[$i] eq $arr[$i]){
                print $arr[$i],": ",$arr[$i+1]," | ",$brr[$i+1],"\n";
        }
}