// Find the inverse of a 2x2 matrix using the following method. Swap the
// diagonals. Change the sign of the non-diagonal elements. Find the determinant
// of this new matrix. Multiply each term of the new matrix by the inverse of the
// determinant. This is the inverse of the matrix. Check that this is the inverse
// by multiplying with itself
// 
// Author:rahule@cse.iitk.ac.in

#include<stdio.h>
main()
{
  float a[2][2],det,a_inv[2][2],I[2][2];
  printf("enter the 2x2 matrix\n");
  scanf("%f%f%f%f",&a[0][0],&a[0][1],&a[1][0],&a[1][1]);	//reading 2x2 matrix
    
  det=a[0][0]*a[1][1]-a[0][1]*a[1][0];	//calculating the determinant
   printf("\n the determinant is %f\n",det);

  //finding the inverse
  
  a_inv[0][0]=a[1][1];	//swapping the diagonals
  a_inv[1][1]=a[0][0];
  a_inv[0][1]=(-1)*a[0][1];	//changing the sign of non-diagonal elements
  a_inv[1][0]=(-1)*a[1][0];
  
  printf("\nafter swapping and changing the diagonals the matrix becomes :\n");
  printf("%f   %f\n%f   %f\n",a_inv[0][0],a_inv[0][1],a_inv[1][0],a_inv[1][1]);
  
  if(det==0)	//if determinant is zero,inverse can not be found
  {
    printf("\nthe determinant of the matrix is zero.cannot find the inverse!exiting..");
  }
  else
  {
    a_inv[0][0]=a_inv[0][0]/det;	//calculating inverse
    a_inv[0][1]=a_inv[0][1]/det;
    a_inv[1][0]=a_inv[1][0]/det;
    a_inv[1][1]=a_inv[1][1]/det;
    
    printf("\nthe inverse of the matrix is :\n");	//prints the inverse
    printf("%f   %f\n%f   %f\n",a_inv[0][0],a_inv[0][1],a_inv[1][0],a_inv[1][1]);
    
    printf("\nmultiplying the matrix with its inverse,we get :\n");	//calculating the value of a*a_inverse
    I[0][0]=a[0][0]*a_inv[0][0]+a[0][1]*a_inv[1][0];
    I[0][1]=a[0][0]*a_inv[0][1]+a[0][1]*a_inv[1][1];
    I[1][0]=a[1][0]*a_inv[0][0]+a[1][1]*a_inv[1][0];
    I[1][1]=a[1][0]*a_inv[0][1]+a[1][1]*a_inv[1][1];
    
    printf("%f   %f\n%f   %f\n",I[0][0],I[0][1],I[1][0],I[1][1]);
  }
}
    
//note that multiplying a matrix with its inverse always results in an identitymatrix