Matrix is idempotent or not.

Posted on Apr 26, 2020

C program to check whether matrix is idempotent or not.

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.

Note: it is important that an involutory matrix should be a square matrix. Because for the multiplication of two matrices the number of rows of the first matrix should be equal to the number of columns of the second matrix. so, for multiplication of a matrix with itself, it is only possible when a matrix is a square matrix.

Program

#include<stdio.h>
#include<conio.h>
#define MAX 10

void read_matrix(int mat[MAX][MAX], int row, int col)
{
    int i, j;
    for(i=0;i<row;i++)
    {
        for(j=0;j<col;j++)
        {
            printf("Element [%d][%d]\t:",i,j);
            scanf("%d",&mat[i][j]);
        }
    }
}

void print_matrix(int mat[MAX][MAX], int row, int col)
{
    int i, j;
    for(i=0;i<row;i++)
    {
        for(j=0;j<col;j++)
        {
            printf("%d\t",mat[i][j]);
        }
        printf("\n");
    }
}

void multiply(int mat[MAX][MAX], int mat1[MAX][MAX], int mul[MAX][MAX], int row)
{
    int i, j, k;

    for(i=0;i<row;i++)
    {
        for(j=0;j<row;j++)
        {
            mul[i][j] = 0;
            for(k=0;k<row;k++)
            {
                mul[i][j] = mul[i][j] + (mat[i][k] * mat1[k][j]);
            }
        }
    }
}

int equal(int mat[MAX][MAX], int mul[MAX][MAX], int row)
{
    int i, j;

    for(i=0;i<row;i++)
    {
        for(j=0;j<row;j++)
        {
            if(mat[i][j] != mul[i][j])
            {
                return(0);
            }
        }
    }

    return(1);
}

int idempotent(int mat[MAX][MAX], int row)
{
    int i, j, flag, mul[MAX][MAX];

    multiply(mat, mat, mul, row);
    flag = equal(mat, mul, row);

    return(flag);
}

void main()
{
    int mat[MAX][MAX];
    int row, col;

    printf("Enter the number of rows or columns of the square matrix\t:");
    scanf("%d",&row);
    col = row;

    printf("Enter the elements of the matrix\n");
    read_matrix(mat, row, col);

    printf("\nMatrix entered is\n");
    print_matrix(mat, row, col);

    if(idempotent(mat, row))
        printf("\nMatrix is an idempotent matrix");
    else
        printf("\nMatrix is not an idempotent matrix");

    getch();
}

Output

********** Run1 ********** 

Enter the number of rows or columns of the square matrix        :3
Enter the elements of the matrix
Element [0][0]  :2
Element [0][1]  :-2
Element [0][2]  :-4
Element [1][0]  :-1
Element [1][1]  :3
Element [1][2]  :4
Element [2][0]  :1
Element [2][1]  :-2
Element [2][2]  :-3

Matrix entered is
2       -2      -4
-1      3       4
1       -2      -3

Matrix is an idempotent matrix


********** Run2 ********** 

Enter the number of rows or columns of the square matrix        :3
Enter the elements of the matrix
Element [0][0]  :1
Element [0][1]  :2
Element [0][2]  :-3
Element [1][0]  :4
Element [1][1]  :5
Element [1][2]  :-6
Element [2][0]  :-7
Element [2][1]  :8
Element [2][2]  :9

Matrix entered is
1       2       -3
4       5       -6
-7      8       9

Matrix is not an idempotent matrix