iptables nat works on connections. The first packet of the connection passes through the nat tables and is translated according to them. Later packets belonging to the same connection do not pass through the nat tables they are simply translated accoridng to the rules established when the first packet was translated.

The iptables man page https://linux.die.net/man/8/iptables documents that the nat table is consulted for "the first packet of a connection" and the documentation for the DNAT and SNAT target says "(and all future packets in this connection will also be mangled)".

Does iptables implicitly and automatically add the reverse/inverse rules for every NAT rule that is added explicitly?

Not exactly

Your first two quotes are correct, the third is confused ramblings of someone who doesn't understand how the system works.

iptables nat (unlike iptables filtering) works on connections. The first packet of the connection passes through the nat tables and is translated according to it. Later packets belonging to the same connection do not pass through the nat tables they are simply translated accoridng to the rules established when the first packet was translated.

The iptables man page https://linux.die.net/man/8/iptables documents that the nat table is consulted for "the first packet of a connection" and the man page section for the DNAT and SNAT target say "(and all future packets in this connection will also be mangled)".

Unfortunately I haven't seen any official documentation which goes into more depth than that. My go-to reference for iptables is the frozentux iptables tutorial but I don't think it's official.

iptables nat works on connections. The first packet of the connection passes through the nat tables and is translated according to them. Later packets belonging to the same connection do not pass through the nat tables they are simply translated accoridng to the rules established when the first packet was translated.

iptables nat works on connections. The first packet of the connection passes through the nat tables and is translated according to them. Later packets belonging to the same connection do not pass through the nat tables they are simply translated accoridng to the rules established when the first packet was translated.

The iptables man page https://linux.die.net/man/8/iptables documents that the nat table is consulted for "the first packet of a connection" and the documentation for the DNAT and SNAT target says "(and all future packets in this connection will also be mangled)".