Append a new associative element to each row of a 2d array

Following is the output of my multidimensional array $csmap_data

Array
(
    [0] => Array
        (
            [cs_map_id] => 84
            [cs_subject_id] => 1
        )

    [1] => Array
        (
            [cs_map_id] => 85
            [cs_subject_id] => 5
        )

    [flag] => 1
)

Initially, there was no [flag] => 1 key-value in the array. I added it to the array $csmap_data.

Ultimately, I want to add the [flag] => 1 in the above two array elements -- not as a separate array element. In short I wanted following output:

Array
    (
        [0] => Array
            (
                [cs_map_id] => 84
                [cs_subject_id] => 1
                [flag] => 1
            )
    
        [1] => Array
            (
                [cs_map_id] => 85
                [cs_subject_id] => 5
                [flag] => 1
            )
       )

The code I was trying to achieve this is as follows, but couldn't get the desired output:

if (!empty($csmap_data)) {  
    foreach ($csmap_data as $csm) {
        $chapter_csmap_details = $objClassSubjects->IsClassSubjectHasChapters($csm['cs_map_id']);
        $csmap_data['flag'] = 1;                            
    }
}

<?
 foreach($csmap_data as $key => $csm)
 {
  $csmap_data[$key]['flag'] = 1;
 }

That should do the trick.