As already pointed out, b += 1 updates b in-place, while a = a + 1 computes a + 1 and then assigns the name a to the result (now a does not refer to a row of A anymore).
To understand the += operator properly though, we need also to understand the concept of mutable versus immutable objects. Consider what happens when we leave out the .reshape:
C = np.arange(12)
for c in C:
c += 1
print(C) # [ 0 1 2 3 4 5 6 7 8 9 10 11]
We see that C is not updated, meaning that c += 1 and c = c + 1 are equivalent. This is because now C is a 1D array (C.ndim == 1), and so when iterating over C, each integer element is pulled out and assigned to c.
Now in Python, integers are immutable, meaning that in-place updates are not allowed, effectively transforming c += 1 into c = c + 1, where c now refers to a new integer, not coupled to C in any way. When you loop over the reshaped arrays, whole rows (np.ndarray's) are assigned to b (and a) at a time, which are mutable objects, meaning that you are allowed to stick in new integers at will, which happens when you do a += 1.
It should be mentioned that though + and += are meant to be related as described above (and very much usually are), any type can implement them any way it wants by defining the __add__ and __iadd__ methods, respectively.