You can check the execution time to get clear picture of it
In [2]: import numpy as np
In [3]: A = np.array([[2, 2],[2, 2]])
In [7]: %timeit np.square(A)
1000000 loops, best of 3: 923 ns per loop
In [8]: %timeit A ** 2
1000000 loops, best of 3: 668 ns per loop