Incorrect output matrix using Strassen's algorithm with numpy matrices

Question

I am attempting to implement Strassen's matrix multiplication algorithm as described in CLRS using Python 3 and numpy matrices.

The issue is that the output matrix C is returned as a zero matrix instead of the correct product. I am not sure why my implementation is not working, but suspect that is has something to do with the creation of the C matrix with each recursive call. I would appreciate any explanation as to what I'm doing wrong and how I can fix it.

Thank you!

import numpy as np

def strassen(A,B):
    n = A.shape[0]
    C = np.zeros((n*n), dtype=np.int).reshape(n,n)
    if n == 1:
        C[0][0] = A[0][0] * B[0][0]

    else:
        k = int(n/2) 

        A11,A21,A12,A22 = A[:k,:k], A[k:, :k], A[:k, k:], A[k:, k:]
        B11,B21,B12,B22 = B[:k,:k], B[k:, :k], B[:k, k:], B[k:, k:]
        C11,C21,C12,C22 = C[:k,:k], C[k:, :k], C[:k, k:], C[k:, k:]

        S1 = B12 - B22
        S2 = A11 + A12
        S3 = A21 + A22
        S4 = B21 - B11
        S5 = A11 + A22
        S6 = B11 + B22
        S7 = A12 - A22
        S8 = B21 + B22
        S9 = A11 - A21
        S10= B11 + B12

        P1 = strassen(A11, S1)
        P2 = strassen(S2, B22)
        P3 = strassen(S3, B11)
        P4 = strassen(A22, S4)
        P5 = strassen(S5, S6)
        P6 = strassen(S7, S8)
        P7 = strassen(S9, S10)

        C11 = P5 + P4 - P2 + P6
        C12 = P1 + P2
        C21 = P3 + P4
        C22 = P5 + P1 - P3 - P7


    return C

Answer 1

OK I got it to work by simply updating the slices C[:k,:k] with new values instead of creating new variables C11, C12 ..ect. since doing so creates a new matrix and is not a reference to the original matrix C.