ARP (Address Resolution Protocol) explained

sir , for the scenario
Computer A ——-Switch1—–ROUTER1——————ROUTER 2 —- Switch2 —– Computer B.

you said that

"Computer A will do an ARP request for the IP address of Router 1

Computer B will do an ARP request for Router 2 (its default gateway).

Router 1 and Router 2 will do ARP requests on the link that connects them to discover each others MAC addresses."

please rectify/guide me if i am worng
computer A will send ARP request to R1 to know R1 MAC address, so whenever it sends send data to ComputerB it will then send it to MAC address of R1.

sir my second query is that MAC address is required at Local area communication , so why R1 and R1 need to know MAC Address of each other since Router works at L3 (IP).