Here are some troubleshooting steps that may help in solving the issue.
- Start by uninstalling/reinstalling the Touchpad driver of the laptop.
- Go to Device Manager and uninstall the Touchpad driver.
- Once uninstalled, download and install the latest driver from ASUS Support site.
- Reboot the laptop once the latest driver has been installed.
- After the reboot do test it again and see if the same problem will persist or not.
- If it doesn't work try connecting an external USB mouse and see if the left or right click works.
- If the external mouse will work then it's a hardware problem, replacing the Touchpad would be the only solution.