However, when you enter the ls $-$a command on the directory where the file is located, you still see the file listed with the following permissions:

$-$rwxr$-$xr$-$x

Why is the file still listed?

answer

You have not rebooted the Linux system to remove the file.

You have not removed the inode for the file.

There is still a hard link associated with the file data.

There is still a soft link associated with the file data.