That's a particularly confusing example to choose, because matrix squaring produces the same result as array (element-wise) squaring: >>> np.array([[1, 0], [

That's a particularly confusing example to choose, because matrix squaring produces the same result as array (element-wise) squaring: >>> np.array([[1, 0], [0, 1]])**2 array([[1, 0], [0, 1]]) Here: >>> np.array([[1, 2], [3, 4]])**2 array([[ 1, 4], [ 9, 16]]) >>> np.mat([[1, 2], [3, 4]])**2 matrix([[ 7, 10], [15, 22]]) The real problem with the np.array("asdgh")**2 example is squaring doesn't make sense for character data. Matrix vs. array squaring has other issues too, as matrix squaring only works with square matrices: >>> np.mat([1, 2])**2 [...] LinAlgError: Last 2 dimensions of the array must be square >>> np.array([1, 2])**2 array([1, 4])