Yes, that is right from the Router. If you have a Cisco router then the command is show arp and you can view all the Mac addresses from the devices attached in toyr network and also see their accosiated ip addresses.
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Should an IT person be able to know where to find a list of all IP addresses and associated MAC addresses on their network?
If the "IT person" works with networking, then probably yes. Many other IT persons have no need to know anything about MAC addresses at all and possibly not even about IP addresses.