**Python program to multiply two matrices** has been shown here. Matrix $[A]_{m \times n}$ can be multiplied with matrix $[B]_{p \times q}$, iff $n = p$ i.e. the number of columns of the first matrix should to be equal to the number of rows in the second matrix. The order of the resultant matrix $C$ would be $m \times q$.

Algorithm, pseudocode and time complexity of the program have also been shown below.

## 1. Algorithm for matrix multiplication

1. Take two matrice $A_{m\times n}$ and $B_{p\times q}$ as input.

2. Declare another matrix $C_{m\times q}$ and initailize it with 0.

3. Check if $n = p$

4. If step [3] is false then display "Matrices can not be multiplied!" and go to step [8]

5. If step [3] is true, then

6. Repeat for each $i \in [0, m - 1]$

6.1. Repeat for each $j \in [0, q - 1]$

6.1.1. Repeat for each $k \in [0, p - 1]$

6.1.1.1. Perform $C[i][j] = C[i][j] + A[i][k] * B[k][j]$

7. Display $C_{m\times q}$ as the resultant matrix.

8. Exit program.

## 2. Pseudocode for matrix multiplication

**Input**: Two matrices $A_{m\times n}$ and $B_{p\times q}$

**Output**: $A * B$

1. **Procedure** matrixMultiplication($A_{m\times n}$, $B_{p\times q}$):

2.

3. **If** $n == p$:

4. **Repeat** for each $i \in [0, m-1]$

5. **Repeat** for each $i \in [0, q-1]$

6. **Repeat** for each $k \in [0, p-1]$

7.

8. **Return** $C_{m\times q}$

9. **Else:**

10. ** Return ***Matrices can not be multiplied!*

11. **End Procedure**

## 3. Time Complexity for matrix multiplication

**Time Complexity:** **O($n^3$)**

Where $n$ is the row and column size of two matrices.

## 4. Python Program for matrix multiplication

# ****************************************** # alphabetacoder.com # Python Program for Matrix Multiplication # ****************************************** # declare a function which takes # two matrices as inputs and returns # the resultant matrix after multiplication def matrixMultiplication(A, B): # get the size of resultant matrix x = len(A) y = len(B[0]) # declare and initialize resultant matrix C = [[0 for j in range(y)] for i in range(x)] # do matrix multiplication for i in range(0, x): for j in range(0, y): for k in range(0, len(B)): # Use len(B) to get the number of rows in B C[i][j] += A[i][k] * B[k][j] return C def main(): # take input of the order of first matrix m = int(input("Enter the number of rows of the first matrix: ")) n = int(input("Enter the number of columns of the first matrix: ")) # take input of the order of second matrix p = int(input("Enter the number of rows of the second matrix: ")) q = int(input("Enter the number of columns of the second matrix: ")) # check if number of columns in the first matrix # is the same as the number of rows in the second matrix. # If not, then matrices cannot be multiplied if n != p: print("Matrices cannot be multiplied!") else: # declare and initialize the matrices A = [[0 for j in range(n)] for i in range(m)] B = [[0 for j in range(q)] for i in range(p)] # take input of the first matrix print("Enter the first matrix of order", m, "x", n, ":") for i in range(m): for j in range(n): A[i][j] = int( input(f"Enter element at row {i + 1} and column {j + 1}: ") ) # take input of the second matrix print("Enter the second matrix of order", p, "x", q, ":") for i in range(p): for j in range(q): B[i][j] = int( input(f"Enter element at row {i + 1} and column {j + 1}: ") ) # call the function to get the resultant matrix # after matrix A is multiplied by matrix B C = matrixMultiplication(A, B) # display matrix C print("The resultant matrix after multiplication: ") # display the result for i in range(m): for j in range(q): print(C[i][j], end=" ") # new line print("") # drive code main()

Output

Enter the number of rows of the first matrix: 3

Enter the number of columns of the first matrix: 3

Enter the number of rows of the second matrix: 3

Enter the number of columns of the second matrix: 3

Enter the first matrix of order 3 x 3 :

Enter element at row 1 and column 1: 5

Enter element at row 1 and column 2: 6

Enter element at row 1 and column 3: 1

Enter element at row 2 and column 1: 0

Enter element at row 2 and column 2: 2

Enter element at row 2 and column 3: 0

Enter element at row 3 and column 1: 3

Enter element at row 3 and column 2: 4

Enter element at row 3 and column 3: 6

Enter the second matrix of order 3 x 3 :

Enter element at row 1 and column 1: 0

Enter element at row 1 and column 2: 1

Enter element at row 1 and column 3: 2

Enter element at row 2 and column 1: 5

Enter element at row 2 and column 2: 3

Enter element at row 2 and column 3: 4

Enter element at row 3 and column 1: 5

Enter element at row 3 and column 2: 0

Enter element at row 3 and column 3: 6

The resultant matrix after multiplication:

35 23 40

10 6 8

50 15 58