Java Program to Check if a Matrix is Invertible

This is the java program to check whether the matrix is invertible or not. The square matrix is invertible if and only if its determinant is non zero.

Here is the source code of the Java Program to Check if a Matrix is Invertible. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

//This is a simple program to check whether the matrix is invertible or not.

//The complexity of the algorithm is O(n^3)

```
 
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```
import java.util.*;
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```
 
```
```
public class Invertible_Matrix 
```
```
{
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    public double determinant(double A[][],int N)

```
    {
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        double det=0;
```
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        if(N == 1)
```
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        {
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```
            det = A[0][0];
```
```
        }
```
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        else if (N == 2)
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        {
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            det = A[0][0]*A[1][1] - A[1][0]*A[0][1];

```
        }
```
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        else
```
```
        {
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            det=0;
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            for(int j1=0;j1<N;j1++)
```
```
            {
```

                double[][] m = new double[N-1][];

                for(int k=0;k<(N-1);k++)

```
                {
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                    m[k] = new double[N-1];

```
                }
```
```
                for(int i=1;i<N;i++)
```
```
                {
```
```
                    int j2=0;
```

                    for(int j=0;j<N;j++)

```
                    {
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                        if(j == j1)
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                            continue;
```

                        m[i-1][j2] = A[i][j];

```
                        j2++;
```
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                    }
```
```
                }
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                det += Math.pow(-1.0,1.0+j1+1.0)* A[0][j1] * determinant(m,N-1);

```
            }
```
```
        }
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        return det;
```
```
    }
```
```
 
```

    public static void main(String args[])

```
    {
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        Scanner input = new Scanner(System.in);

        System.out.println("Enter the order of the square matrix");

```
        int n = input.nextInt();
```
```
 
```

        System.out.println("Enter the elements of the square matrix");

        double[][] mat = new double[n][n];

```
        for(int i=0; i<n; i++)
```
```
        {
```
```
            for(int j=0; j<n; j++)
```
```
            {
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                mat[i][j] = input.nextDouble();

```
            }
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```
        }
```
```
 
```

        Invertible_Matrix I = new Invertible_Matrix();

```
 
```
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        if(I.determinant(mat, n) == 0)
```
```
        {
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            System.out.println("Matrix is not Invertible, as the determinant is : "+I.determinant(mat, n));

```
        }
```
```
        else
```
```
        {
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            System.out.println("Matrix is Invertible, as the determinant is : "+I.determinant(mat, n));

```
        }
```
```
 
```
```
        input.close();
```
```
	}
```
```
}
```

Output:

$ javac Invertible_Matrix.java
$ java Invertible_matrix
Enter the order of the square matrix: 
3
Enter the elements of the square matrix: 
1 2 3
4 5 6
7 8 9
Matrix is not Invertible, as the determinant is : 0.0

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