Finding the inverse of a matrix.

Here’s an example of a Java program that finds the inverse of a matrix using the Gauss-Jordan elimination method:

  import java.util.Arrays;

   public class MatrixInverse {

    public static double[][] findInverse(double[][] matrix) {

        int n = matrix.length;

        double[][] augmentedMatrix = new double[n][2 * n];

        // Create an augmented matrix by appending an identity matrix

        for (int i = 0; i < n; i++) {

            System.arraycopy(matrix[i], 0, augmentedMatrix[i], 0, n);

            augmentedMatrix[i][i + n] = 1;

        }

        // Apply Gauss-Jordan elimination

        for (int i = 0; i < n; i++) {

            // Pivot for the current row

            double pivot = augmentedMatrix[i][i];

            // Divide the current row by the pivot

            for (int j = 0; j < 2 * n; j++) {

                augmentedMatrix[i][j] /= pivot;

            }

            // Eliminate other rows

            for (int j = 0; j < n; j++) {

                if (j != i) {

                    double factor = augmentedMatrix[j][i];

                    for (int k = 0; k < 2 * n; k++) {

                        augmentedMatrix[j][k] -= factor * augmentedMatrix[i][k];

                    }
              }

            }
        }

        // Extract the inverse matrix from the augmented matrix

        double[][] inverseMatrix = new double[n][n];

        for (int i = 0; i < n; i++) {

            System.arraycopy(augmentedMatrix[i], n, inverseMatrix[i], 0, n);

        }

        return inverseMatrix;

    }

    public static void main(String[] args) {

        double[][] matrix = {

            {1, 2, 3},

            {4, 5, 6},

            {7, 8, 9}

        };

        double[][] inverse = findInverse(matrix);

        System.out.println("Original Matrix:");

        printMatrix(matrix);

        System.out.println("Inverse Matrix:");

        printMatrix(inverse);

    }

    public static void printMatrix(double[][] matrix) {

        for (double[] row : matrix) {

            System.out.println(Arrays.toString(row));

        }

       System.out.println();
    }
}

This program defines a `findInverse` method that takes a square matrix as input and returns its inverse. The `main` method demonstrates the usage of the `findInverse` method by finding the inverse of a 3×3 matrix and printing both the original matrix and its inverse.

Note that this implementation assumes the input matrix is non-singular (i.e., it has an inverse). Additionally, it is always good practice to add additional error checking and validation for real-world applications.