Example: Check if a given Matrix is an Identity Matrix in C++

// Check if a given Matrix is an Identity Matrix
#include <iostream>
#include <vector> // Using std::vector for dynamic matrices

using namespace std;

// Function to check if a matrix is an identity matrix
bool isIdentityMatrix(const vector<vector<int>>& matrix) {
    int rows = matrix.size();
    if (rows == 0) { // Empty matrix is not an identity matrix
        return false;
    }
    int cols = matrix[0].size();

    // Step 1: Check if the matrix is square
    if (rows != cols) {
        return false; // Not a square matrix, so cannot be an identity matrix
    }

    // Step 2: Iterate through the matrix elements
    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            // Step 3: Check diagonal elements
            if (i == j) {
                if (matrix[i][j] != 1) {
                    return false; // Diagonal element is not 1
                }
            }
            // Step 4: Check non-diagonal elements
            else {
                if (matrix[i][j] != 0) {
                    return false; // Non-diagonal element is not 0
                }
            }
        }
    }

    // Step 5: If all checks pass, it's an identity matrix
    return true;
}

int main() {
    // Example 1: Identity Matrix
    vector<vector<int>> matrix1 = {
        {1, 0, 0},
        {0, 1, 0},
        {0, 0, 1}
    };
    cout << "Matrix 1 is " << (isIdentityMatrix(matrix1) ? "an Identity Matrix" : "NOT an Identity Matrix") << endl;

    // Example 2: Not an Identity Matrix (off-diagonal not zero)
    vector<vector<int>> matrix2 = {
        {1, 2, 0},
        {0, 1, 0},
        {0, 0, 1}
    };
    cout << "Matrix 2 is " << (isIdentityMatrix(matrix2) ? "an Identity Matrix" : "NOT an Identity Matrix") << endl;

    // Example 3: Not an Identity Matrix (diagonal not one)
    vector<vector<int>> matrix3 = {
        {1, 0, 0},
        {0, 5, 0},
        {0, 0, 1}
    };
    cout << "Matrix 3 is " << (isIdentityMatrix(matrix3) ? "an Identity Matrix" : "NOT an Identity Matrix") << endl;

    // Example 4: Not an Identity Matrix (not square)
    vector<vector<int>> matrix4 = {
        {1, 0},
        {0, 1},
        {0, 0}
    };
    cout << "Matrix 4 is " << (isIdentityMatrix(matrix4) ? "an Identity Matrix" : "NOT an Identity Matrix") << endl;

    // Example 5: Not an Identity Matrix (empty matrix)
    vector<vector<int>> matrix5;
    cout << "Matrix 5 is " << (isIdentityMatrix(matrix5) ? "an Identity Matrix" : "NOT an Identity Matrix") << endl;

    // Example 6: 1x1 Identity Matrix
    vector<vector<int>> matrix6 = {{1}};
    cout << "Matrix 6 is " << (isIdentityMatrix(matrix6) ? "an Identity Matrix" : "NOT an Identity Matrix") << endl;

    return 0;
}