The Nexus 9 is still a new device, but it's a Nexus, and that means developers are going to tinker with it. In order to flash ROMs and whatnot, you need a custom recovery. Now there is one for this device. An official build of TWRP is live, and it brings some changes that take into account Lollipop's new security measures.
Here's the changelog for TWRP 220.127.116.11.
- Pull in all changes from Android 5.0 lollipop into TWRP
- Add decrypt support for Android 5.0 lollipop encrypted partitions including automatic decrypt when the default_password is in use
- Revert some changes to exFAT that were breaking exFAT support on some devices
- Other minor fixes and updates
Installing TWRP on a Nexus device is pretty easy. All you need is ADB/fastboot on your computer and an unlocked bootloader. The image files are available on the TWRP site, but make sure you grab the newest one. Good luck and happy flashing.