C weird array syntax in multi-dimensional arrays

Question

I've known that this is true:

x[4] == 4[x]

What is the equivalent for multi-dimensional arrays? Is the following true?

x[4][3] == 3[x[4]] == 3[4[x]]

Answer 1

x[y] is defined as *(x + (y))

x[y][z] would become *(*(x + (y)) + z)

x[y[z]] would become *(x + (*(y + (z))))

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x[4][3] would become *(*(x + (4)) + 3) would become *(*(x + 4) + 3)

3[x[4]] would become *(3 + (*(x + (4)))) would become *(*(x + 4) + 3)

3[4[x]] would become *(3 + (*(4 + (x)))) would become *(*(x + 4) + 3)

Which means they are all equivalent.

Answer 2

Yes. In each case x is an array which decays to a pointer and then has pointer arithmetic performed on it.