Need Matrix multiplication assistance - python-3.x

Question

So I have these three complete functions that return the desired row of a matrix, column of a matrix, and dot product of the row and column, and I need to somehow mesh them together in a fourth function in order to find the product of two matrices being multiplied together. Any suggestions?
#Test matrices
A = [[2,4], [7,0], [6,3]]
B = [[3,1], [-1,8], [-3, 3]]
C = [[4,1,9], [6,2,8], [7,3,5]]
D = [[2,9], [5,2], [1,0]]
def row(A,i):
Z = []
Z.append(A[i])
return Z[0]
def col(B,j):
Z=[]
for i in range(len(B)):
Z.append(B[i][j])
return Z
def dotProduct(x,y):
prod=0
for i in range(len(x)):
prod=prod+x[i]*y[i]
return prod
def matrixMUL(A, B):
Z = []
....
return Z

Answer 1

Solution with 3 more auxiliary functions:
from functools import partial
#Test matrices
A = [[2,4], [7,0], [6,3]]
B = [[3,1], [-1,8], [-3, 3]]
C = [[4,1,9], [6,2,8], [7,3,5]]
D = [[2,9], [5,2], [1,0]]
def row(A,i):
Z = []
Z.append(A[i])
return Z[0]
def col(B,j):
Z=[]
for i in range(len(B)):
Z.append(B[i][j])
return Z
def dotProduct(x,y):
prod=0
for i in range(len(x)):
prod=prod+x[i]*y[i]
return prod
def shape(A):
num_rows = len(A)
num_cols = len(A[0]) if A else 0
return num_rows, num_cols
def matrix_product_entry(A, B, i, j):
return dotProduct(row(A, i), col(B, j))
def matrix_make(rows, cols, entry_fn):
return [[entry_fn(i, j) for j in range(cols)]
for i in range(rows)]
def matrixMUL(A, B):
n1, k1 = shape(A)
print(n1, k1)
n2, k2 = shape(B)
if k1 != n2:
raise ArithmeticError("matrices shapes are not compatible!")
return matrix_make(n1, k2, partial(matrix_product_entry, A, B))
print (matrixMUL(C, D))
# returns [[22, 38], [30, 58], [34, 69]]