/** * * In linear algebra a matrix M[][] is said to be a symmetric matrix if and only if transpose of the matrix is equal to the matrix itself. A transpose of a matrix is when we flip the matrix over its diagonal, which resultant switches its row and columns indices of the matrix. Below the example of Symmetric matrix − ⎡⎣⎢147456769⎤⎦⎥⇒⎡⎣⎢147456769⎤⎦⎥ The above matrix is the symmetric matrix we took the matrix on the left and transpose it and the result is same is equal to the matrix itself. Example Input: arr1[][n] = { { 1, 2, 3 }, { 2, 2, 4 }, { 3, 4, 1 } }; Output: its a symmetric matrix Input: arr1[][n] = { { 1, 7, 3 }, { 2, 9, 5 }, { 4, 6, 8 } }; Output: its not a symmetric matrix Approach We can just follow these steps − 1. Take a matrix and store its transpose in other matrix. 2. Check the resultant matrix is same as the input matrix. ➡️Algorithm⤵️ Start Step 1 -> define macro as #define n 10 Step 2 -> declare function to find transporse of a matrix void transpose(int arr1[][n], int arr2[][n], int a) Loop For int i = 0 and i < a and i++ Loop For int j = 0 and j < a and j++ Set arr2[i][j] = arr1[j][i] End End Step 3 -> declare function to check symmetric or not bool check(int arr1[][n], int a) declare variable as int arr2[a][n] Call transpose(arr1, arr2, a) Loop For int i = 0 and i < a and i++ Loop For int j = 0 and j < a and j++ IF (arr1[i][j] != arr2[i][j]) return false End End End Return true Step 4 -> In main() Declare variable as int arr1[][n] = { { 1, 2, 3 }, { 2, 2, 4 }, { 3, 4, 1 } } IF (check(arr1, 3)) Print its a symmetric matrix Else Print its not a symmetric matrix Stop ➡️Example⤵️ * * **/ #include #define n 10 using namespace std; //find transporse of a matrix void transpose(int arr1[][n], int arr2[][n], int a){ for (int i = 0; i < a; i++) for (int j = 0; j < a; j++) arr2[i][j] = arr1[j][i]; } //check symmetric or not bool check(int arr1[][n], int a){ int arr2[a][n]; transpose(arr1, arr2, a); for (int i = 0; i < a; i++) for (int j = 0; j < a; j++) if (arr1[i][j] != arr2[i][j]) return false; return true; } int main(){ int arr1[][n] = { { 1, 2, 3 }, { 2, 2, 4 }, { 3, 4, 1 } }; if (check(arr1, 3)) cout << "its a symmetric matrix"; else cout << "its not a symmetric matrix"; return 0; } /** * * Output: its a symmetric matrix * * **/

[TUTORIAL] ➡️ symmetric-matrix