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Java Program to Check Whether a Matrix is Symmetric or Not
  • Last Updated : 13 Jan, 2021

A symmetric matrix is a square matrix in which the transpose of the square matrix is the same as the original square matrix. A square matrix is a matrix in which the number of columns is the same as the number of rows. If the matrix is a symmetric matrix then it is also a square matrix but vice versa isn’t true. Matrix is simply considered as 2D arrays for action to be performed. Here, we are going to see the approach to check if the entered square matrix is symmetric or not.

Illustration:

Input : 6 5 2
        5 0 9
        2 9 3
Output: The matrix is symmetric

Input : 6 1 2
        5 0 9
        2 9 3
Output: The matrix is not symmetric

Approach: 

  • Take the matrix as an input from the user
  • Find transpose of the matrix
  • Compare two matrices
  • If the two matrices is the same then it is symmetric otherwise it’s not.

Implementation:

Example



Java

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// Java Program to check whether matrix is
// symmetric or not
  
// Importing all classes of
// java.util package
import java.util.*;
  
// Class
public class GFG {
    // Matrix 1
  
    // Method to check whether the matrix is
    // symmetric or asymmetric
    static void checkSymmetric(int mat[][], int row,
                               int col)
    {
        int i, j, flag = 1;
  
        // Display message
        System.out.println("The matrix formed is:");
  
        // Nested for loop for matrix iteration
  
        // Outer loop for rows
        for (i = 0; i < row; i++) {
            // Inner loop for columns
            for (j = 0; j < col; j++) {
                // Print matrix
                System.out.print(mat[i][j] + "\t");
            }
  
            System.out.println("");
        }
  
        // Matrix 2
  
        // Finding transpose of the matrix
        int[][] transpose = new int[row][col];
  
        // Again, nested for loop for matrix iteration
  
        // Outer loop for rows
        for (i = 0; i < row; i++) {
  
            // Inner loop for columns
            for (j = 0; j < col; j++) {
  
                // Print matrix elements
                transpose[j][i] = mat[i][j];
            }
        }
  
        // Condition check over Matrix 1 with Matrix 2
  
        if (row == col) {
  
            // Outer loop for rows
            for (i = 0; i < row; i++) {
  
                // Inner loop for columns
                for (j = 0; j < col; j++) {
  
                    // Comparing two matrices
                    if (mat[i][j] != transpose[i][j]) {
                        flag = 0;
                        break;
                    }
                }
  
                // Setting a flag value for symmetric matrix
                if (flag == 0) {
  
                    // Display message
                    System.out.print(
                        "\nThe matrix is not symmetric");
                    break;
                }
            }
  
            // Setting a flag value different from above
            // for symmetric matrix
            if (flag == 1) {
  
                // Display message
                System.out.print(
                    "\nThe matrix is symmetric");
            }
        }
  
        // If it isn't a square matrix
        // then it can't be a symmetric matrix
        else {
  
            // Display message
            System.out.print(
                "\nThe matrix is not symmetric");
        }
    }
  
    // Main driver method
    public static void main(String args[])
    {
        // Taking input from the user
        Scanner sc = new Scanner(System.in);
  
        // Declaring variables and setting flag to 1
        int i, j, row, col, flag = 1;
  
        // Taking input from the user
        System.out.print("Enter the number of rows:");
        row = sc.nextInt();
  
        // Display message
        System.out.print("Enter the number of columns:");
  
        // Reading matrix elements individually using
        // nextInt() method
        col = sc.nextInt();
  
        // Declaring a 2D array(matrix)
        int[][] mat = new int[row][col];
  
        // Display message
        System.out.println("Enter the matrix elements:");
  
        // Nested for loop for traversing matrix
  
        // Outer loop for rows
        for (i = 0; i < row; i++) {
  
            // Inner loop for colummns
            for (j = 0; j < col; j++) {
  
                // Print matrix element
                mat[i][j] = sc.nextInt();
            }
        }
  
        // calling function made above to check
        // whether matrix is symmetric or not
        checkSymmetric(mat, row, col);
    }
}

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Output: Below both symmmericity and asymetricity is checked as follows:


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