Why is this the inverse of a Enigma Machine rotor? I am learning about how the Enigma Machine works and I found this example of one letter being encrypted by an Enigma Machine. It shows the letter "G" going through three rotors and then it goes into the reflector, then back into the inverse rotors. This is where I get confused.

The rotors are

Rotor I:   BDFHJLCPRTXVZNYEIWGAKMUSQO
Rotor II:  AJDKSIRUXBLHWTMCQGZNPYFVOE
Rotor III: EKMFLGDQVZNTOWYHXUSPAIBRCJ
Reflector: ABCDEFGHIJKLMNOPQRSTUVWXYZ  # not sure if this matters
           YRUHQSLDPXNGOKMIEBFZCWVJAT


I would think that the inverse of the rotors would just be each rotor reversed like this.

Inversed Rotor I:   OQSUMKAGWIEYNZVXTRPCLJHFDB
Inversed Rotor II:  EOVFYPNZGQCMTWHLBXURISKDJA
Inversed Rotor III: JCRBIAPSUXHYWOTNZVQDGLFMKE


but on the example I linked to

Inversed Rotor I:   TAGBPCSDQEUFVNZHYIXJWLRKOM
Inversed Rotor II:  AJPCZWRLFBDKOTYUQGENHXMIVS
Inversed Rotor III: UWYGADFPVZBECKMTHXSLRINQOJ


I don't see any relation between the rotor and the inversed versions of them. So, is this example wrong, or am I missing something?
The example is using a shorthand notation for the rotors that somewhat obscures the way they actually work.  For example, the first rotor in your example, BDFHJLCPRTXVZNYEIWGAKMUSQO, actually applies the following permutation of the alphabet:

ABCDEFGHIJKLMNOPQRSTUVWXYZ
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
BDFHJLCPRTXVZNYEIWGAKMUSQO


Applying this rotor in the reverse direction thus, obviously, gives the inverse permutation:

BDFHJLCPRTXVZNYEIWGAKMUSQO
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
ABCDEFGHIJKLMNOPQRSTUVWXYZ


Now, the same inverse permutation can also be written equivalently as:

ABCDEFGHIJKLMNOPQRSTUVWXYZ
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
TAGBPCSDQEUFVNZHYIXJWLRKOM


You can check that these are, indeed, the same permutation: both map A &rarr; T, B &rarr; A, C &rarr; G, and so on.  The only difference is the order in which the individual input/ouput letter pairs are listed: in the first version, they are sorted by the output letter, while in the second version they are sorted by the input letter.

Now, the page you're reading is using a shorthand notation where the permutations are always sorted by the input letter, and only the output letters are actually shown.  This gives a nice and compact notation, but it does make it a bit harder to e.g. see whether two permutations are actually inverses of each other.