Pointer question

[slewis at oregon.uoregon.edu]

Hello netters.

I have a question about pointers.  Well, actually I have a few observations
and I'm not sure if they're correct.  Maybe you can help...

Assume the following variables:

int i,j;
int **p, *a, *b;

Also assume that we have allocated space for a 2D n X m int "array" (p), 
a n-length linear array (a) and an m-length linear array (b) in the 
following manner:

p = (int **) malloc(n*sizeof(int *));
for(i=0; i < n; i++) p[i] = (int *) malloc(m*sizeof(int));

and

a = (int *) malloc(n*sizeof(int));
b = (int *) malloc(m*sizeof(int));

Now, we may use p[i][j], a[i] and b[i] to refer to the elements of these 
arrays.

My understanding is that a[i] is equiv to *(a+i).  Now, this 
implies some strange things, right?  First, since (pointer) addition is
commutative,  a[i] == *(a+i) == i[a].  I've seen this stated before in
this newsgroup.

But are the following assertions true:

1.  p[i][j] == *( *(p+i) + j) == j[p[i]] == j[i[p]] 

2.  a[b[i]] == *( a + *(b+i)) == b[i][a] == i[b][a]

(assuming that b[i] contains a valid [-1 < b[i] < n] number)

If so, I think I understand.  If not, I'm confused.

Scott