JSFiddle - React, Tailwind, and code Playground

HTML

<table>
    <tbody>
        <tr>
           <td>01</td><td>02</td><td>03</td><td>04</td> 
        </tr> 
        <tr>
           <td>05</td><td>06</td><td>07</td><td>08</td>
        </tr>
         <tr>
           <td>09</td><td>10</td><td>11</td><td>12</td>
        </tr>  
        <tr>
            <td>13</td><td>14</td><td>15</td><td>16</td>
        </tr>
    </tbody>
</table>

JavaScript

function swap( cells, x, y ){
   if( x != y ){     
 
   var $cell1 = cells[y][x];
   var $cell2 = cells[x][y];
   $cell1.replaceWith( $cell2.clone() );
   $cell2.replaceWith( $cell1.clone() );
    }
}

var cells = [];
$('table').find('tr').each(function(){
    var row = [];
    $(this).find('td').each(function(){
       row.push( $(this) );    
    });
    cells.push( row );
});

for( var y = 0; y <= cells.length/2; y++ ){
    for( var x = 0; x < cells[y].length; x++ ){
        swap( cells, x, y );
    }   
}