RSVP to an event with Apps mail
If you're invited by someone to an event with Google Calendar, you may receive an email with the text of the invitation.
Please note: You don't always receive an email if the organizer chooses not to send the email or if you have turned off email notifications for new events.
If you're an Apps mail user, you can RSVP to the event directly through the email invitation by clicking on one of the links (Yes, No or Maybe).
You can also go to the event's page and leave a comment next to your RSVP status as mentioned previously.
RSVP to an event from other email applications
If your friends are using another email application (such as Microsoft Outlook, Hotmail, Yahoo!, etc.) to read and reply to your Google Calendar invitation, make sure they use the 'Yes/No/Maybe' links in the body of the invitation itself rather than the response buttons provided by their email application.
Currently, when guests respond using the email application's reply buttons, the event is only updated if it's scheduled on your primary calendar.
This means that someone using Microsoft Outlook should not use the Outlook reply tools, but rather the 'Yes/No/Maybe' links that are included in the email notification.
Reference RSVP to an event with Apps mail
What do you do after you select yes, maybe, or no? I'm not clear on how that works. I selected maybe on an invitation, and the screen with my calendar appeared. How do I know the message went back to the sender? I ended up just replying to the email, which is fine too. You might show the result after selecting one of the options. Thanks.