If you can use the stack for that data (small volume) then you usually define the matrix:
int matrix[X][Y]
When you want to allocate it in the heap (large volume), the you usually define a:
int** matrix = NULL;
and then allocate the two dimensions with malloc/calloc.
You can treat the 2d array as int** but that is not a good practice since it makes the code less readable. Other then that
**matrix == matrix[0][0] is true