C++| adjoint of 2X2 and 3X3 matrix

Hello peeps! Lord Hypersonic greets you. Today I am presenting a new c++ program that can calculate adjoint of both types of the matrix (i.e 2x2 and 3x3 matrix).

It uses a simple technique to calculate the adjoint, which we use in maths to calculate adjoints.

Header files included:-

iostream: For using input and output stream (cout as output stream OR for printing output on the screen, and cin as input stream OR for taking data from user).
conio.h: For using _getch() function (it is a function to take input from the user as a single character).

Variables used:-

A2 (a 2D array of 2x2) of integer data-type.
AD2 (a 2D array of 2x2) of integer data-type.
C2 ( a 2D array of 2x2) of integer data-type.
A3 (a 2D array of 3x3) of integer data-type.
AD3 (a 2D array of 3x3) of integer data-type.
C3 (a 2D array of 3x3) of integer data-type.
ch of integer data-type.
i of integer data-type (for different for loops, the scope is different).

Working:-

First, the user is asked to provide the order of the matrix, for which he/she want to find adjoint. The input for this given by the user is stored in ch.
If the input provided by the user is 1 (which is for the 2x2 matrix), the user is asked to provide elements of the 2x2 matrix. The elements of the matrix provided by the user are stored in A2.
After taking elements of the matrix, cofactors of a given matrix is calculated. For a 2x2 matrix, cofactors can be calculated like this:-
for example, the given matrix is :
A = | 1 2 |
| 3 4 |
Then cofactors (C) will be :
C= | 4 -3 |
| -2 1 |
For common, cofactors for 2x2 matrix is calculated as, C[i][j]=(-1)^(i+j)*(element of A at another end of diagonal). The cofactos calculated is stored in C2.
After cofactors are calculated, we calculate the adjoint of a matrix. Adjoint is actually a matrix in which the elements in the rows of cofactors will be in the stored in adjoint matrix AD2 as columns. For example:-
C = | 4 -3 |
| -2 1 |
then adjoint is:-
J = | 4 -2 |
| -3 1 |
After calculating Adjoint AD2, it prints the elements of AD2.
This is how we calculate adjoint of a 2x2 matrix. But if the user enters 2 instead of 1 in ch, which means he wants to find the adjoint of a 3x3 matrix, then calculations will be like this.
Before proceeding, I am assuming you know how to find minors of a 3x3 matrix and how to find cofactors using minors.
First, the user will be asked to enter the elements of the 3x3 matrix for which they want to find adjoint. Input will be stored in A3.
After taking input, minors are calculated. After finding minors, cofactors are calculated in C3. Formula to calculating cofactors is C_ij = (-1)^(i+j)* M_ij
In this program, I am directly using this formula to find cofactors in both cases.
After calculating cofactors, We find adjoint in the same manner as we have calculated in a 2x2 matrix and will be stored in AD3.
After adjoint AD3 is calculated. Print the elements of AD3.

This is how you can make a c++ program to calculate adjoint of 3x3 and 2x2 matrix. If you have any query then ask in comments, or you can join my Discord server and can ask me there. Link for my discord server is given in About me page.

Source Code:-

/*

Program: an Adjoint calculator for 2X2 and 3X3 square matrix.
Author: Lord Hypersonic
Email: lordhypersonic.522@gmail.com
Website: www.lordhypersonic.blogspot.in

*/

#include <iostream>
#include <conio.h>

using namespace std;

int main()
{
int ch,A2[2][2],AD2[2][2],C2[2][2],A3[3][3],AD3[3][3],C3[3][3];
cout<<"Find adjoint of :- \n1. 2x2 matrix \n2. 3x3 matrix \n>"; cin>>ch;
if (ch==1) //if user want to find the adjoint of matrix of order 2x2
{
cout<<"Enter elements of A matrix: \n";
//loop for entering elements of matrix A of order 2x2.
for (int i=0; i<2; i++)
{
for (int j=0; j<2; j++)
{
cout<<"A["<<i+1<<"]["<<j+1<<"] : "; cin>>A2[i][j];
}
}
//Calculating cofactors of a matrix of order 2x2
C2[0][0]=A2[1][1]; C2[0][1]=-A2[1][0]; C2[1][0]=-A2[0][1]; C2[1][1]=A2[0][0];
//calculating adjoint of the matrix of order 2x2
AD2[0][0]=C2[0][0]; AD2[0][1]=C2[1][0]; AD2[1][0]=C2[0][1]; AD2[1][1]=C2[1][1];
cout<<"\n\nAdjoint of A is :- \n\n";
cout<<"|\t"<<AD2[0][0]<<"\t"<<AD2[0][1]<<"\t|\n|\t"<<AD2[1][0]<<"\t"<<AD2[1][1]<<"\t|\n";
}
else if (ch==2) //if user wants to calculate the adjoint of a matrix of order 3x3
{

cout<<"Enter elements of A matrix: \n";
//loop for entering elements of matrix A of order 3x3.
for (int i=0; i<3; i++)
{
for(int j=0; j<3; j++)
{
cout<<"A["<<i+1<<"]["<<j+1<<"] : "; cin>>A3[i][j];
}
}
//calculating cofactors of matrix A of order 3x3
C3[0][0]=((A3[1][1]*A3[2][2])-(A3[2][1]*A3[1][2])); C3[0][1]=-((A3[1][0]*A3[2][2])-(A3[2][0]*A3[1][2]));
C3[0][2]=((A3[1][0]*A3[2][1])-(A3[2][0]*A3[1][1]));
C3[1][0]=-((A3[0][1]*A3[2][2])-(A3[2][1]*A3[0][2])); C3[1][1]=((A3[0][0]*A3[2][2])-(A3[2][0]*A3[0][2])); C3[1][2]=-((A3[0][0]*A3[2][1])-(A3[2][0]*A3[0][1]));
C3[2][0]=((A3[0][1]*A3[1][2])-(A3[1][1]*A3[0][2])); C3[2][1]=-((A3[0][0]*A3[1][2])-(A3[1][0]*A3[0][2]));
C3[2][2]=((A3[0][0]*A3[1][1])-(A3[1][0]*A3[0][1]));
// calculating adjoint of matrix A of order 3x3
AD3[0][0]=C3[0][0]; AD3[0][1]=C3[1][0]; AD3[0][2]=C3[2][0];
AD3[1][0]=C3[0][1]; AD3[1][1]=C3[1][1]; AD3[1][2]=C3[2][1];
AD3[2][0]=C3[0][2]; AD3[2][1]=C3[1][2]; AD3[2][2]=C3[2][2];
//printing values of adjoint A of order 3x3.
cout<<"Adjoint A is:-\n\n";
cout<<"|\t"<<AD3[0][0]<<"\t"<<AD3[0][1]<<"\t"<<AD3[0][2]<<"\t|\n";
cout<<"|\t"<<AD3[1][0]<<"\t"<<AD3[1][1]<<"\t"<<AD3[1][2]<<"\t|\n";
cout<<"|\t"<<AD3[2][0]<<"\t"<<AD3[2][1]<<"\t"<<AD3[2][2]<<"\t|\n";
}
/*
| 00 01 02 |
| 10 11 12 |
| 20 21 22 |
*/
else cout<<"No such choice exist ...... "<<endl; //if the user enters another key other than 1 and 2.
_getch(); //waiting for the user to press any key to exit.
return 0;

}

Working of the program is given below.