For one thing you are missing quotes arround associative index names. Since the array elements are complex variables you should also enclose them in curly braces to get them parsed properly in a double quoted string. Another issue is that you echo the if condition which is not right. Then you are missing a space before selected
and the angle bracket after the selected goes to the next echo statement (otherwise it might get lost). See my attempt at the correct code:
echo "<option value=\"{$row['province']\"";
if($_POST['prov'] == $row['province']) {
echo ' selected="selected"'
}
echo ">{$row['province']}</option>";