# Java Program to Find the Determinant of a Matrix

This is the Java Program to Find the Modulus of a Matrix.

Problem Description

Given a square matrix, find and print the modulus(determinant) of the matrix.
Example:
Matrix:
1 2 3
4 5 6
7 8 9

Output:
Modulus = 0

Problem Solution

The algorithm for calculating modulus of 3*3 matrix is
x=(matrix[0][0] * (matrix[1][1] * matrix[2][2] – matrix[1][2] * matrix[2][1]));
y=(matrix[0][1] * (matrix[1][0] * matrix[2][2] – matrix[1][2] * matrix[2][0]));
z=(matrix[0][2] * (matrix[1][0] * matrix[2][1] – matrix[1][1] * matrix[2][0]));

determinant= x – y + z;

Program/Source Code

Here is the source code of the Java Program to Find the Modulus of a Matrix. The program is successfully compiled and tested using IDE IntelliJ Idea in Windows 7. The program output is also shown below.

1. ` `
2. `//Java Program to Find the Modulus of a `
3. ` `
4. `import java.io.BufferedReader;`
5. `import java.io.InputStreamReader;`
6. ` `
7. `public class ModulusOfAMatrix {`
8. `    // Function to read array elements and calculate the determinant`
9. `    public static void main(String[] args) {`
10. `        BufferedReader br= new BufferedReader(new InputStreamReader(System.in));`
11. `        int order=3;`
12. `        int[][] matrix=new int[3][3];`
13. `        System.out.println("Enter the elements of 3x3 matrix");`
14. `        int i,j;`
15. `        for(i=0;i<matrix.length;i++){`
16. `            for(j=0;j<matrix[i].length;j++){`
17. `                try{`
18. `                    matrix[i][j]=Integer.parseInt(br.readLine());`
19. `                }`
20. `                catch(Exception e){`
21. `                    System.out.println("An error occured. Please retry");`
22. `                    return;`
23. `                }`
24. `            }`
25. `        }`
26. `        int determinant,x,y,z;`
27. `        x=(matrix[0][0] * (matrix[1][1] * matrix[2][2]`
28. `                       - matrix[1][2] * matrix[2][1]));`
29. `        y=(matrix[0][1] * (matrix[1][0] * matrix[2][2]`
30. `                       - matrix[1][2] * matrix[2][0]));`
31. `        z=(matrix[0][2] * (matrix[1][0] * matrix[2][1]`
32. `                       - matrix[1][1] * matrix[2][0]));`
33. `        determinant= x - y + z;`
34. `        System.out.println("The modulus of the given matrix is "+ determinant);`
35. ` `
36. `    }`
37. `}`
Program Explanation

1. In function main(), a matrix is entered.
2. Then in variables x, y and z various coefficients are calculated.
3. Finally, the statement (determinant= x – y + z), calculates the determinant and it is displayed.

Time Complexity: O(1).

Runtime Test Cases
```
Case 1 (Simple Test Case):

Enter the elements of 3x3 matrix
1
2
3
4
5
6
7
8
9
The modulus of the given matrix is 0

Case 2 (Simple Test Case - another example):

Enter the elements of 3x3 matrix
12
43
5
23
56
7
45
2
65
The modulus of the given matrix is -19598```

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