Associativity of ++ and --

The following question stems from p.132 in the book "The C Programming
Language", second edition by K & R.

The have

struct {
int len;
char *str;
} *p;

The question is how come parentheses are need when you go like:
(++p)->len;

but you don't need them when you go:
p++->len;

The only thing I can think of would be that in the former, the prefix
operator associates right to left,
whereas in the former, the postfix operator associates left to right.
I'm I close?

Chad

.