Here one bank in L3 represents one core, so each core has its own directory in L3 to maintain the record of the cache lines in L2.

In my understanding, L1 will also have to keep a similar record of cache lines somewhere in the cache system?

"L3 is an inclusive cache" --> does it mean whenever we modify data in L2 cache, we need to propagate it to L3 cache? This sounds like a huge cost...