Python Program to check idempotent matrix

Given a N * N matrix and the task is to check matrix is idempotent matrix or not.
Idempotent matrix: A matrix is said to be idempotent matrix if matrix multiplied by itself return the same matrix. The matrix M is said to be idempotent matrix if and only if M * M = M. In idempotent matrix M is a square matrix.

Examples: 

Input : mat[][] = {{3, -6},  {1, -2}};
Output: Idempotent Matrix

Input : mat[N][N] = {{2, -2, -4}, {-1, 3, 4}, {1, -2, -3}}
Output : Idempotent Matrix.

Python 3

# Python Program to check given matrix
# is idempotent matrix or not.
import math

# Function for matrix multiplication.
def multiply(mat, res):

    N= len(mat)
    for i in range(0,N):

        for j in range(0,N):

            res[i][j] = 0
            for k in range(0,N):
                res[i][j] += mat[i][k] * mat[k][j]

# Function to check idempotent
# property of matrix.
def checkIdempotent(mat):

    N= len(mat)
    # Calculate multiplication of matrix
    # with itself and store it into res.
    res =[[0]*N for i in range(0,N)]
    multiply(mat, res)

    for i in range(0,N):
        for j in range(0,N):
            if (mat[i][j] != res[i][j]):
                return False
    return True

# driver Function
mat = [ [2, -2, -4],
        [-1, 3, 4],
        [1, -2, -3] ]

# checkIdempotent function call.
if (checkIdempotent(mat)):
    print("Idempotent Matrix")
else:
    print("Not Idempotent Matrix.")

# This code is contributed by Gitanjali.

Output

Idempotent Matrix

Time Complexity: O(N³)
Auxiliary Space: O(N²)

Please refer complete article on Program to check idempotent matrix for more details!

Using Numpy:

Install Numpy using command

pip install numpy

This method converts the matrix to a numpy array and uses the @ operator to perform matrix multiplication. The all() function is used to check if all elements in the comparison are True.

Python3

import numpy as np

def is_idempotent(matrix):
    # Convert the matrix to a numpy array
    arr = np.array(matrix)
    # Check if the matrix multiplied by itself is equal to the original matrix
    return (arr @ arr == arr).all()

matrix = [[3, -6], [1, -2]]
print(is_idempotent(matrix))  # True

matrix = [[2, -2, -4], [-1, 3, 4], [1, -2, -3]]
print(is_idempotent(matrix))  # True

matrix = [[1, 2], [3, 4]]
print(is_idempotent(matrix))  # False
#This code is contributed by Edula Vinay Kumar Reddy

Output:

True
True
False

Time complexity: O(n^2)
Auxiliary Space: O(n^2)