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