If I have a 100 Mbps (Ethernet) Router, but a Gigabit Switch will my LAN data tranfer speed be 100 Mpbs or 1000 Mbps ?

This is a diagram of how networking structure is going to look like.

I am pretty sure that data transfer from Client A to Client D will be at 100 Mpbs, But i am not sure regarding the Transfer speed between Client A and Client B / Client C which are all connected to the network via a Gigabit Switch, Will it be 100 Mbps or will it be 1000Mbps ? I am talking about LAN data transfer only, i know my Internet / WAN speeds will be limited to 100 mbps.

I am planning have a Gigabit LAN, i am wondering if it is possible to do it without upgrading the router.