All hope is not lost @Kernel_Panic
@Apollonius code will restore the correct permissions to sudoers.so
However, since you can no longer use sudo to become root on your system, you will have to do so from a live-dvd or a live-usb, which ever you used to install Ubuntu-Mate.
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When booting into a live session, pick "Try Ubuntu-Mate before installing"
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Once to boot process is complete, open Caja (file manager) and navigate to /usr/lib/sudo/ on your computers hard drive.
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Then right click and select "Open Terminal from here"
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Then in the terminal enter
sudo chmod 644 sudoers.so -
Followed by
sudo chown -R root:root sudoers.so
After all that reboot into your regular system, open a terminal, and enter sudo su
If all went well, you should be prompted for a password, which means sudoers.so has the correct permissions and sudo is now working again.
If your going to continue to use Linux, you will eventually need to brush up on your terminal skills. This idea people have today that the command line is no longer needed in Linux is just not true.
http://linuxcommand.org/ is a very good place to start.
Once you have some basic command skills mastered, I think you will find that Linux is a much more versatile operating system than you realized.