Explanation
The PATH environment variable is a colon-separated list of directories that the shell searches for commands.
To add a new directory to the PATH, you need to append it to the existing value of the variable, using the syntax PATH=new/dir:PATH. However, this only changes the PATH for the current shell session. To make the change permanent, you need to use the export command, which makes the variable available to all child processes of the shell. The export command takes the name of the variable as an argument, without the dollar sign ($). Therefore, the correct command to add /new/dir/ to the PATH and export it is export PATH=/new/dir:PATH. References:
* Linux Essentials - Linux Professional Institute (LPI)
* How to set the path and environment variables in Windows - Computer Hope

Explanation
In Linux, every file and directory is associated with an owner and a group. The owner is the user who created the file or directory, and the group is the group to which the owner belongs. Therefore, each file is owned by exactly one user and one group. This is true for option A. The other options are false for the following reasons:
* Option B: The owner of a file does not always have full permissions when accessing the file. The permissions are determined by the file mode, which can be changed by the owner or the root user. The file mode specifies the read, write, and execute permissions for the owner, the group, and others. The owner can have different permissions than the group or others.
* Option C: The user owning a file does not have to be a member of the file's group. The owner can change the group ownership of the file to any group on the system, regardless of whether the owner belongs to that group or not. However, only the root user or a user with the CAP_CHOWN capability can change the group ownership to a group that the owner is not a member of.
* Option D: When a user is deleted, all files owned by the user do not disappear. The files remain on the system, but their owner is changed to an invalid user ID (UID). The files can still be accessed by the group or others, depending on the permissions. The files can also be reclaimed by the root user or a user with the CAP_CHOWN capability, who can change the owner to a valid user.
* Option E: The owner of a file can be changed once it is assigned to an owner. The owner can transfer the ownership to another user, or the root user or a user with the CAP_CHOWN capability can change the owner to any user on the system. The command to change the owner of a file is chown. References: 1: Chown Command in Linux (File Ownership) | Linuxize 2 3: Linux File Permissions and Ownership Explained with Examples 4 2: 3 Ways to Find File Owner in Linux - howtouselinux 1

Explanation
The correct command to change the ownership of the file doku.odt to a new owner named tux is chown tux doku.odt. This command uses the chown command, which stands for change owner, followed by the name of the new owner and the name of the file as arguments. The chown command allows you to change the user and/or group ownership of a given file, directory, or symbolic link12. The other options are incorrect because they use different commands or syntax that do not change the ownership of the file. For example:
* Option A uses the chmod command, which stands for change mode, and is used to change the permissions of files and directories, not the ownership3.
* Option B uses the newuser command, which is used to create a new user account, not to change the ownership of a file4.
* Option D uses the transfer command, which is not a valid Linux command.
* Option E uses the passwd command, which is used to change the password of a user account, not the ownership of a file5.
References: 1: Chown Command in Linux (File Ownership) | Linuxize 2: chown command in Linux with Examples - GeeksforGeeks 3: Chmod Command in Linux (File Permissions) | Linuxize 4: newusers(8) - Linux man page 5: passwd(1) - Linux man page