How do I correctly set up, access, and free a multidimensional array in C?

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In C since C99, even dynamic multidimensional arrays can be easily allocated in one go with malloc and freed with free:

double (*A)[n] = malloc(sizeof(double[n][n]));

for (size_t i = 0; i < n; ++i)
  for (size_t j = 0; j < n; ++j)
      A[i][j] = someinvolvedfunction(i, j);

free(A);

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