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.
Â
Examples:Â
Â
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.
Â
Java
// Java program to check given matrix// is idempotent matrix or not.import java.io.*;Â
class GFG{    static int N = 3;         // Function for matrix multiplication.    static void multiply(int mat[][], int res[][])    {        for (int i = 0; i < N; i++)        {            for (int j = 0; j < N; j++)            {                res[i][j] = 0;                for (int k = 0; k < N; k++)                    res[i][j] += mat[i][k] * mat[k][j];            }        }    }         // Function to check idempotent    // property of matrix.    static boolean checkIdempotent(int mat[][])    {        // Calculate multiplication of matrix        // with itself and store it into res.        int res[][] = new int[N][N];        multiply(mat, res);             for (int i = 0; i < N; i++)        {            for (int j = 0; j < N; j++)            {                if (mat[i][j] != res[i][j])                    return false;            }        }        return true;    }Â
    // Driver code.    public static void main (String[] args)    {        int mat[][] = {{2, -2, -4},                       {-1, 3, 4},                       {1, -2, -3}};             // checkIdempotent function call.        if (checkIdempotent(mat))            System.out.println( "Idempotent Matrix");        else            System.out.println("Not Idempotent Matrix.");             }}Â
// This code is contributed by vt_m. |
Output:
Idempotent Matrix
Time complexity: O(N3)
Auxiliary space: O(N2)
Please refer complete article on Program to check idempotent matrix for more details!
