Matrix multiplication is an operation that takes two matrices as input and produces single matrix by multiplying rows of the first matrix to the column of the second matrix.In matrix multiplication make sure that the number of rows of the first matrix should be equal to the number of columns of the second matrix.
Example: Multiplication of two matrices by each other of size 3×3.
Input:matrix1 = ([1, 2, 3], [3, 4, 5], [7, 6, 4]) matrix2 = ([5, 2, 6], [5, 6, 7], [7, 6, 4]) Output : [[36 32 32] [70 60 66] [93 74 100]]
Methods to multiply two matrices in python
1.Using explicit for loops: This is a simple technique to multiply matrices but one of the expensive method for larger input data set.In this, we use nested for loops to iterate each row and each column.
If matrix1 is a n x m matrix and matrix2 is a m x l matrix.
# input two matrices of size n x m matrix1 = [[ 12 , 7 , 3 ],
[ 4 , 5 , 6 ],
[ 7 , 8 , 9 ]]
matrix2 = [[ 5 , 8 , 1 ],
[ 6 , 7 , 3 ],
[ 4 , 5 , 9 ]]
res = [[ 0 for x in range ( 3 )] for y in range ( 3 )]
# explicit for loops for i in range ( len (matrix1)):
for j in range ( len (matrix2[ 0 ])):
for k in range ( len (matrix2)):
# resulted matrix
res[i][j] + = matrix1[i][k] * matrix2[k][j]
print (res)

Output:
[[114 160 60] [ 74 97 73] [119 157 112]]
In this program, we have used nested for loops for computation of result which will iterate through each row and column of the matrices, at last it will accumulate the sum of product in the result.
2. Using Numpy : Multiplication using Numpy also know as vectorization which main aim to reduce or remove the explicit use of for loops in the program by which computation becomes faster.
Numpy is a build in a package in python for arrayprocessing and manipulation.For larger matrix operations we use numpy python package which is 1000 times faster than iterative one method.
For detail about Numpy please visit the Link
# We need install numpy in order to import it import numpy as np
# input two matrices mat1 = ([ 1 , 6 , 5 ],[ 3 , 4 , 8 ],[ 2 , 12 , 3 ])
mat2 = ([ 3 , 4 , 6 ],[ 5 , 6 , 7 ],[ 6 , 56 , 7 ])
# This will return dot product res = np.dot(mat1,mat2)
# print resulted matrix print (res)

Output:
[[ 63 320 83] [ 77 484 102] [ 84 248 117]]
Using numpy
# same result will be obtained when we use @ operator # as shown below(only in python >3.5) import numpy as np
# input two matrices mat1 = ([ 1 , 6 , 5 ],[ 3 , 4 , 8 ],[ 2 , 12 , 3 ])
mat2 = ([ 3 , 4 , 6 ],[ 5 , 6 , 7 ],[ 6 , 56 , 7 ])
# This will return matrix product of two array res = mat1 @ mat2
# print resulted matrix print (res)

Output:
[[ 63 320 83] [ 77 484 102] [ 84 248 117]]
In the above example we have used dot product and in mathematics the dot product is an algebraic operation that takes two vectors of equal size and returns a single number. The result is calculated by multiplying corresponding entries and adding up those products.
This article is contributed by Dheeraj Sharma. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.
To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course.
Recommended Posts:
 Multiply matrices of complex numbers using NumPy in Python
 Calculate inner, outer, and cross products of matrices and vectors using NumPy
 Transpose a matrix in Single line in Python
 Python program to Reverse a single line of a text file
 Python program to add two Matrices
 Python program to add two matrices
 Python program to multiply two matrices
 Python List Equality  Program to check if two given matrices are identical
 Read a file line by line in Python
 NumPy  Vector Multiplication
 Matrix Multiplication in NumPy
 NumPy  3D matrix multiplication
 Program for addition of two matrices
 Program to check if two given matrices are identical
 Kronecker Product of two matrices
 Count pairs from two sorted matrices with given sum
 Find the intersection of two Matrices
 Minimum elements to be added so that two matrices can be multiplied
 Java Program to Multiply two Matrices of any size
 Java Program to Add two Matrices
Improved By : AkshanshSaxena