DNS for private network - should router be the DNS server?

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http://serverfault.com – I want to set up BIND for a private subdomain on a private network, like in the question here: How to configure bind for a private subdomain? My question is this - should my (linux) router act as the DNS server for this? Or should I have a seperate machine on the network acting as the DNS server? Does it not matter as long as all the machines on the network are configured to resolve to the internal DNS server? (HowTos)