Let A be a square matrix of size n x n. Consider the following program.

Which of the following option is correct regarding function CheckMatrix ?
(A) CheckMatrix() checks if matrix idempotent
(B) CheckMatrix() checks if matrix involutory
(C) CheckMatrix() checks if matrix invertible
(D) CheckMatrix() checks if matrix symmetric


Answer: (B)

Explanation: Give program checks if matrix involutory: A * A = I:

// Program to implement involutory matrix.
#include
#define N 3
using namespace std;

// Function for matrix multiplication.
void multiply(int mat[][N], int res[][N])
{
for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { res[i][j] = 0; for (int k = 0; k < N; k++) res[i][j] += mat[i][k] * mat[k][j]; } } } // Function to check involutory matrix. bool InvolutoryMatrix(int mat[N][N]) { int res[N][N]; // multiply function call. multiply(mat, res); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { if (i == j && res[i][j] != 1) return false; if (i != j && res[i][j] != 0) return false; } } return true; } // Driver function. int main() { int mat[N][N] = { { 1, 0, 0 }, { 0, -1, 0 }, { 0, 0, -1 } }; // Function call. If function return // true then if part will execute otherwise // else part will execute. if (InvolutoryMatrix(mat)) cout << \"Involutory Matrix\"; else cout << \"Not Involutory Matrix\"; return 0; } [/sourcecode] So, option (B) is correct.

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