In the METHOD 1 above, rptr turned out to be a pointer to type "one dimensional array of COLS integers". It turns out that there is syntax which can be used for this type without the need of typedef. If we write: 

      int (*xptr)[COLS]; 

the variable xptr will have all the same characteristics as the variable rptr in METHOD 1 above, and we need not use the typedef keyword. Here xptr is a pointer to an array of integers and the size of that array is given by the #defined COLS. The parenthesis placement makes the pointer notation predominate, even though the array notation has higher precedence. i.e. had we written

      int *xptr[COLS];

we would have defined xptr as an array of pointers holding the number of pointers equal to that #defined by COLS. That is not the same thing at all. However, arrays of pointers have their use in the dynamic allocation of two  dimensional arrays, as will be seen in the next 2 methods.