It's (actually not)

G.

In any column or row, there are only 4 unique patterns:

1) XXX

2) XXY

3) XYX

4) XYZ

(Ignoring YXX as nothing but a reflection of XXY)

Putting the patterns in a (row, column) pair, the given matrices are as follows:

(444, 234) (233, 423) (243, 242)

(242, 342) (423, 334) (213, 433)

(433, 312) (224, 231) (???, ???)

Numbering the collection of matrices as:

1 2 3

4 5 6

7 8 ?

We see that it’s possible to go from 1 to 8 by swapping columns and rows between matrices:

234<>423, 423<>243, 243<>342*;

342<>234, 334<>433, 213<>312*;

312<> 231, ???<>???, ???<>???

*One of two possible transformations

Continuing as best we can, the answer needs to have some permutation of a “123” pattern or a “224” pattern.

The potential answers are as follows:

A – (434, 313)

B – (343, 432)

C – (223, 123)

D – (234, 343)

E – (422, 123)

F – (233, 324)

G – (324, 242)

H – (212, 343)

Therefore the only possible answers are C, E, and G.

If the rules have been explained to you, after casting about for a bit you’ll see that you haven’t got quite the right approach, then notice the “correct” behavior as you examine how the columns transform after eliminating “3” as being redundant (both XXY and XYX have two Xs, XXX as three, XYZ only one.)

If the rules haven’t been explained to you, most importantly that the interval [1,8] is supposed to be linear (…,0,1,2,3,4,5,6,7,8,9…) and not cyclic (…,9,1,2,3,4,5,6,7,8,9,1,…)** you might conclude that G is the only logical choice, as it is the only answer that can transform back to 1. However, if you try to justify the shapes and/or the exact transformation procedure (which row/column goes where) you won’t find a nice and simple rule, which is why C is more correct.

**Dear math nerds: Yes, I know that the integers form an (or the) infinite cyclic group under addition. Let me be colloquial for one damn second.