Touch ID not working after update iOS10.0.2
http://www.macworld.co.uk/how-to/iosapps/ios-10-troubleshooting-tips-3646690/
iOS 10 troubleshooting tips: Touch ID isn't working
Some users have reported that a previously happy Touch ID setup stopped working when they made the update to iOS 10. This is a pain, but rescuable - you will probably need to clear your fingerprints and enter them again.
First, however, try something simpler: go to Settings > Touch ID & Passcode, enter your passcode and then tap the buttons next to Apple Pay and iTunes & App Store so they turn white. Power off your iPhone and turn it back off again, then go back into Settings and turn those two buttons back to green (you'll need to enter your Apple ID password).
Has that fixed the problem? In my case no!
If not, go through the fingerprints stored in Settings > Touch ID & Passcode - tap each one in turn - and tap Delete Fingerprint. Then go back and tap Add A Fingerprint, and put them back in. This is a bit of a hassle, but should fix the problem.
I did it all, but the problem could not be solved.
iPhone 6 Plus, iOS 10.0.2