For elementwise multiplication of matrix objects, you can use numpy.multiply:
import numpy as np
a = np.array([[1,2],[3,4]])
b = np.array([[5,6],[7,8]])
np.multiply(a,b)
Result
array([[ 5, 12],
[21, 32]])
However, you should really use array instead of matrix. matrix objects have all sorts of horrible incompatibilities with regular ndarrays. With ndarrays, you can just use * for elementwise multiplication:
a * b
If you're on Python 3.5+, you don't even lose the ability to perform matrix multiplication with an operator, because @ does matrix multiplication now:
a @ b # matrix multiplication