So, regarding your example, you want to insert the following couples of values :
I,A
I,B
II,A
II,B
III,A
III,B
You'll get a lot of duplicated datas, but, anyway, if you want to insert the datas as previously described ; you can manage that by emebeding the 2 loops. For example :
$countA = count($checkA);
$countB = count($checkB);
for ($i=0;$i<$countA;$i++) {
for($j=0;$j<$countB;$j++){
$sql = "INSERT INTO tbl VALUES ('$checkA[$i]','$checkB[$j]')";
}
}