Let’s learn how to tell if a matrix is symmetric and symmetric matrix program in java.

A square matrix is said to be symmetric if given square matrix is equal to its transpose.

#### Symmetric matrix program in java

**How to determine if a matrix is symmetric?**

For a matrix to be symmetric, first it should be a square matrix and second every element at “i”th row and “j”th column should be equal to every element at “j”th row and “i”th column.

In other words A[x][y] is a square matrix of (3 X 3) order, then A[x][y] matrix is said to be symmetric if every element at “x”th row and “y”th column is equal to element at “y”th row and “x”th column.

Also read – transpose of a matrix

That is A[x][y] == A[y][x]

Let’s see how to check if a matrix is symmetric,

import java.util.Scanner; public class SymmetricMatrixDemo { public static void main(String[] args) { Scanner sc = new Scanner(System.in); System.out.println("Please enter number of rows - "); int row = sc.nextInt(); System.out.println("Please enter number of columns - "); int col = sc.nextInt(); int symMatrix[][] = new int[row][col]; System.out.println("Please enter the elements - "); for(int x = 0; x < row; x++) { for(int y = 0; y < col; y++) { symMatrix[x][y] = sc.nextInt(); } } System.out.println("Now printing the input matrix - "); for(int x = 0; x < row; x++) { for(int y = 0; y < col; y++) { System.out.print(symMatrix[x][y] + "\t"); } System.out.println(); } // check if a matrix is symmetric if(row != col) { System.out.println("It's not a square matrix!!"); } else { boolean symmetricMatrix = true; for(int x = 0; x < row; x++) { for(int y = 0; y < col; y++) { if(symMatrix[x][y] != symMatrix[y][x]) { symmetricMatrix = false; break; } } } if(symmetricMatrix) { System.out.println("It's a symmetric matrix!!"); } else { System.out.println("It's not a symmetric matrix!!"); } } sc.close(); } }

**Output:**

Please enter number of rows – 3

Please enter number of columns – 3

Please enter the elements –

2 4 6 4 1 8 6 8 10

Now printing the input matrix –

2 4 6

4 1 8

6 8 10

It’s a symmetric matrix!!

Also read – sparse matrix and its representation in java