Availability Group Failover General Question

Hello,

I Have Always on Availability group with Windows failover cluster I have 3 nodes and 3 Instances. SQLServerDB01(Primary), SQLServerDB02(Secondary Synchronous), SQLServerDB03(Secondary Asynchronous).

Now when Failover occur on SQLServerDB01(this server out), it will automatic go to server SQLServerDB02 if automatic failover was enabled.

what will happen to the solution will SQLServerDB02 become primary ?? and will it be Read-Only database or Read-Write ??

if the answer was Read-Only is there any way to make it Read-Write.

Regards,

Ayesh.