C programs to check the equality of two matrices have been shown here. Two matrices $[A]_{m \times n}$ and $[B]_{p \times q}$ are considered to be equal if both of the following conditions are satisfied:

(i) Number of rows and columns are same for both of the matrices i.e. $m = p$ and $n = q$

(ii) Each elements of $A$ is equal to corresponding element of $B$ i.e. $A_{ij} = B_{xy}$ for each $i \in m$, $j \in n$, $x \in p$, $y \in q$, $i = x$ and $j = y$.

The algorithm, pseudocode and time complexity of the program have also been shown.

## 1. Algorithm to check the equality of two matrices

1. Take two matrice $A_{m\times n}$ and $B_{p\times q}$

2. Check if $m=p$ and $n=q$

3. If step [2] is false then print "Not equal" and exit the program

4. If step [2] is true, then

5. Check if each corresponding element of $A$ and $B$ are equal

6. If step [5] is true then print "Equal" and exit program

7. If step [5] is false then print "Not equal" and exit program

## 2. Pseudocode to check the equality of two matrices

Input: Two matrices $A_{m\times n}$ and $B_{p\times q}$

Output: Equal or Not equal

1. Procedure matrixEquality($A_{m\times n}$, $B_{p\times q}$):

2. If $m==p$ and $n==q$:

3. If $A_{ij}==B_{ij}$ for each $i \in m$ and $j \in n$:

4. Return Equal

5. Else:

6. Return Not equal

7. Else:

8. Return Not equal

9. End Procedure

## 3. Time Complexity to check the equality of two matrices

Time Complexity: O($mn$)

Where $m$ is the number of rows and $n$ is the number of columns in the matrices.

## 4. C Program to check the equality of two matrices

Code has been copied
/******************************************
Alphabetacoder.com
C program to check equality of two matrices
*******************************************/

#include <stdio.h>

int main() {
// declare variables
int m, n, p, q, flag = 0, i, j;
int A[10][10] = {0}, B[10][10] = {0};

//take input of the order of first matrix
printf("Enter the number of row and column of first matrix = ");
scanf("%d%d", & m, & n);

//take input of the first matrix
printf("Enter the first matrix of order %d x %d = \n", m, n);
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
scanf("%d", & A[i][j]);
}
}
//take input of the order of second matrix
printf("Enter the number of row and column of second matrix = ");
scanf("%d%d", & p, & q);

//take input of the first matrix
printf("Enter the second matrix of order %d x %d = \n", p, q);
for (i = 0; i < p; i++) {
for (j = 0; j < q; j++) {
scanf("%d", & B[i][j]);
}
}

// check if order of matrices are same
// if not same order then matrices are of different order
if (m != p || n != q) {
printf("\nMatrices are of different order, hence not equal");
flag = 1;
} else {
//check equality of each corresponding elements
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
if (A[i][j] != B[i][j]) {
// inequality spotted
printf("\nMatrices are not equal. Element mismatch at row %d, column %d ", i + 1, j + 1);
flag = 1;
break;
}
}
if (flag == 1)
break;
}
}
// if flag = 0, then matrices are equal
if (flag == 0)
printf("\nMatrices are equal");
return 0;
}


Output

#### Case 1:

Enter the number of row and column of first matrix = 3 3

Enter the first matrix of order 3 x 3 =

1 2 3

4 5 6

7 8 9

Enter the number of row and column of second matrix = 2 3

Enter the second matrix of order 2 x 3 =

8 0 5

6 4 1

Matrices are of different order,hence not equal

#### Case 2:

Enter the number of row and column of first matrix = 2 2

Enter the first matrix of order 2 x 2 =

1 2

4 5

Enter the number of row and column of second matrix = 2 2

Enter the second matrix of order 2 x 2 =

1 2

4 5

Matrices are equal

#### Case 3:

Enter the number of row and column of first matrix = 2 2

Enter the first matrix of order 2 x 2 =

1 3

5 6

Enter the number of row and column of second matrix = 2 2

Enter the second matrix of order 2 x 2 =

1 3

5 7

Matrices are not equal. Element mismatch at row 2, column 2

## 5. C Program to check the equality of two matrices using recursion

Code has been copied
/**********************************************************
Alphabetacoder.com
C program to check equality of two matrices using recursion
***********************************************************/
#include <stdio.h>

#define MAXSIZE 10

// Declare a recursive function to check
// equality of two matrices
// This function takes two matices (A and B), Sizes of both matrices (m, n)
// and index of current row & column as  parameters
int check_equality(int A[][MAXSIZE], int B[][MAXSIZE], int m, int n, int row, int col) {

// check if all columns are traversed
// if yes the set col = 0 and increment row
if (col >= n) {
row++;
col = 0;
}

// check if all rows are traversed
if (row >= m)
return 1;

// check equality of corresponding element
// if current element of both matrices are
// not equal then return 0
// If elements are same then go for next element
// by calling the recursive function
if (A[row][col] != B[row][col]) {
printf("\nMatrices are not equal. Element mismatch at row %d, column %d", row + 1, col + 1);
return 0;
} else
return check_equality(A, B, m, n, row, col + 1);
}

int main() {
// declare variables
int m, n, p, q, flag = 0, i, j;
int A[MAXSIZE][MAXSIZE] = {0}, B[MAXSIZE][MAXSIZE] = {0};

//take input of the order of first matrix
printf("Enter the number of row and column of first matrix = ");
scanf("%d%d", & m, & n);

//take input of the first matrix
printf("Enter the first matrix of order %d x %d = \n", m, n);
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
scanf("%d", & A[i][j]);
}
}
//take input of the order of second matrix
printf("Enter the number of row and column of second matrix = ");
scanf("%d%d", & p, & q);

//take input of the first matrix
printf("Enter the second matrix of order %d x %d = \n", p, q);
for (i = 0; i < p; i++) {
for (j = 0; j < q; j++) {
scanf("%d", & B[i][j]);
}
}

// check if order of matrices are same
// if not same order then check each corresponding elements
if (m != p || n != q) {
printf("\nMatrices are of different order, hence not equal");
flag = 1;
} else {
//check equality of each corresponding elements
// by calling a recursive function
// If the function return 1 then the matrices are equal
// If the function return 0 then the matrices are not equal
if (check_equality(A, B, m, n, 0, 0))
printf("\nMatrices are equal");
}

return 0;
}


Output

#### Case 1:

Enter the number of row and column of first matrix = 4 3

Enter the first matrix of order 4 x 3 =

3 2 3

4 1 6

5 8 9

2 7 5

Enter the number of row and column of second matrix = 2 3

Enter the second matrix of order 2 x 3 =

5 0 1

6 4 7

Matrices are of different order,hence not equal

#### Case 2:

Enter the number of row and column of first matrix = 4 3

Enter the first matrix of order 4 x 3 =

3 2 3

4 1 6

5 8 9

2 7 5

Enter the number of row and column of second matrix = 4 3

Enter the second matrix of order 4 x 3 =

3 2 3

4 1 6

5 8 9

2 7 5

Matrices are equal

#### Case 3:

Enter the number of row and column of first matrix = 2 2

Enter the first matrix of order 2 x 2 =

7 8

4 6

Enter the number of row and column of second matrix = 2 2

Enter the second matrix of order 2 x 2 =

7 2

4 6

Matrices are not equal. Element mismatch at row 1, column 2