c program to solve a system of equation using matrix inversion method

 #include <stdio.h>

#include <stdlib.h>

int main()

{

    double A[3][3], B[3][1];

    int n;

    printf("\nEnter size of square Matrix: ");

    scanf("%d", &n);

    printf("\nEnter elements of first Matrix:\n");

    for (int i = 0; i < n; i++)

    {

        for (int j = 0; j < n; j++)

        {

            scanf("%lf", &A[i][j]);

        }

    }

    printf("\nEnter elements of second Matrix:\n");

    for (int j = 0; j < n; j++)

        scanf("%lf", &B[j][0]);

    double inverse[3][3], mul[3][1];

    double det = A[0][0] * (A[1][1] * A[2][2] - A[2][1] * A[1][2]) -

                 A[0][1] * (A[1][0] * A[2][2] - A[2][0] * A[1][2]) +

                 A[0][2] * (A[1][0] * A[2][1] - A[2][0] * A[1][1]);

    // Check if the determinant is non-zero

    if (det == 0)

    {

        printf("The matrix is singular, and its inverse does not exist.\n");

        exit(EXIT_FAILURE);

    }

    // Calculate the adjugate of the matrix

    else

    {

        double adjugate[3][3];

        adjugate[0][0] = A[1][1] * A[2][2] - A[1][2] * A[2][1];

        adjugate[0][1] = A[0][2] * A[2][1] - A[0][1] * A[2][2];

        adjugate[0][2] = A[0][1] * A[1][2] - A[0][2] * A[1][1];

        adjugate[1][0] = A[1][2] * A[2][0] - A[1][0] * A[2][2];

        adjugate[1][1] = A[0][0] * A[2][2] - A[0][2] * A[2][0];

        adjugate[1][2] = A[0][2] * A[1][0] - A[0][0] * A[1][2];

        adjugate[2][0] = A[1][0] * A[2][1] - A[1][1] * A[2][0];

        adjugate[2][1] = A[0][1] * A[2][0] - A[0][0] * A[2][1];

        adjugate[2][2] = A[0][0] * A[1][1] - A[0][1] * A[1][0];

        // Calculate the inverse by dividing the adjugate by the determinant

        for (int i = 0; i < n; i++)

        {

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

            {

                inverse[i][j] = adjugate[i][j] / det;

            }

        }

    }

    double result[3][1];

    for (int i = 0; i < n; i++)

    {

        result[i][0] = 0;

        for (int j = 0; j < n; j++)

        {

            result[i][0] += inverse[i][j] * B[j][0];

        }

    }

    printf("\nResultant Matrix is : \n");

    for (int i = 0; i < n; i++)

    {

        for (int j = 0; j < 1; j++)

        {

            printf("%.2lf\t", result[i][j]);

        }

        printf("\n");

    }

    return 0;

}