You have a syntactic problem in your sql:

$sql = "UPDATE inventory set image='$image', product='$product', category='$category', seller='$seller' WHERE id = $id";

In addition you need to verify if $id has the correct value. Because if it's empty or null your query will fail.

If you want to insert data you can use a query like this:

$sql = "INSERT INTO inventory (image, product, category, seller) VALUES ('$image', '$product', '$category', '$seller')";

Try this in your edit.php view:

<?php
    $sql = "SELECT * FROM inventory WHERE id=".$_REQUEST['id];
      $result = $connection->query($sql);

      if ($result->num_rows > 0) {
        $row = $result->fetch_assoc();
      } else {
        echo "No Results";
      }
      $connection->close();
?>
<div class="row" id="mainSection">
  <form action="update.php" method="post">
    <input type="hidden" name="id" value="value="<?php echo $row['id']?>"">
    <h3>Image:</h3>
        <input type="text" name="image" value="<?php echo $row['image']?>">
    <h3>Product:</h3>
        <input type="text" name="product" value="<?php echo $row['product']?>">
    <h3>Category:</h3>
        <input type="text" name="category" value="<?php echo $row['category']?>">
    <h3>Seller:</h3>
        <input type="text" name="seller" value="<?php echo $row['seller']?>">
    <br><br>
    <input type="submit" value="Update My Record">
  </form>
  <br>
  <a href="admin.php" id="backButton">Back</a>    
</div>

You need to set a value for the id, and then use $_POST['id'] in your query.

First of all the sql syntax for update query is wrong. Secondly there is no value set in the id in the form. So when you post the form the value will be empty.

$sql = "SELECT * FROM inventory";
  $result = $connection->query($sql);

  if ($result->num_rows > 0) {
    while ($row = $result->fetch_assoc()) {
      echo "
      <img src=$row['image'] id='productImage'> <br>
      product: $row['product'];<br>
      category: $row['category']; <br>
      seller: $row['seller'] ;<br>
      <a href="edit.php?id=$row['id']">Edit</a>
      <hr>
      ";
    }
  } else {
    echo "No Results";
  }
  $connection->close();

EDIT.PHP

<div class="row" id="mainSection">
  <?php $id = $_REQUEST['id']; ?>
  <form action="update.php" method="post">

    <input type="hidden" name="id" value="<?=$id?>">

    <h3>Image:</h3>
        <input type="text" name="image">

    <h3>Product:</h3>
        <input type="text" name="product">

    <h3>Category:</h3>
        <input type="text" name="category">

    <h3>Seller:</h3>
        <input type="text" name="seller">

    <br>
    <br>

    <input type="submit" value="Update My Record">

  </form>
  <br>
  <a href="admin.php" id="backButton">Back</a>

</div>

UPDATE.PHP

<?php
$id= $_POST['id'];
$image = $_POST['image'];
$product = $_POST['product'];
$category = $_POST['category'];
$seller = $_POST['seller'];

$sql = "UPDATE inventory set image='".$image."', product='".$product."', category='".$category."', seller='".$seller."' WHERE id = ".$id." ";

if ($connection->query($sql) === true) {
  echo "Inserted Successfully";
} else {
  echo "Error occured in the insert: " . $connection->error;
}

 $connection->close();