It's an older Logitech Tablet Keyboard. This is it:

https://www.amazon.com/gp/product/B009JPBPWO/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1

I certainly did not pay that price, more like $29

I have a similar setup also for school. I use a Bluetooth Logitech Tablet Keyboard and I have an OTG cable that I use occasionally for USB storage and sometimes a spare Logitech wireless (unified) desktop mouse I have lying around. (Also, if you're looking for a case recommendation, I'm using the MoKo cover that a few other people on this sub recomended, and it's been pretty nice--especially for the price)

I find this setup to work pretty well, but the mouse is usually overkill. Another thing to point out with my mouse is that if you don't use it after a very brief period of time, it disconnects into a power saving mode and takes a while to reconnect. A few other notes from my experience with mice on Android is that left, middle and right clicks all act as touch inputs; hover events work in specific applications like Chrome; scrolling works like you'd expect it to; and the back button acts like the system back button (but the forward button is useless, even in Chrome).

I can definitely recommend the keyboard, though. The one I linked to already is a full-sized keyboard with decent keys and shortcuts that work like they say. Alt + Tab also works like on Windows--and it's amazing to say the least. Typing on it still feels a bit weird, and possibly my biggest gripe about it is that if you're holding Shift, the backspace button doesn't do anything.

I'm not really sure how it works to have multiple Bluetooth connections since I haven't really tried it before, but I think that the Nexus 9 supports multiple connections, even to older Bluetooth revisions. My only experience with this, however, is the fact that I once had my tablet connected to my laptop and the keyboard over Bluetooth.