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#include <stdio.h>
#include <stdlib.h>

// Function to initialize the matrix with user input
void initialize(int ***M, int *size) {
    int i, j;

    // Input matrix dimension
    scanf("%d", size);

    // Allocate memory for the matrix
    *M = (int **)malloc(*size * sizeof(int *));
    for (i = 0; i < *size; i++) {
        (*M)[i] = (int *)malloc(*size * sizeof(int));
    }

    // Input matrix elements
    for (i = 0; i < *size; i++) {
        for (j = 0; j < *size; j++) {
            scanf(" %d", &(*M)[i][j]);
        }
    }

}

// Function to output the matrix with size✕size 2D format
void outputMatrix(const int **M, const int size) {
    int i, j;

    for (i = 0; i < size; i++) {
        for (j = 0; j < size; j++) {
            printf("%d ", M[i][j]);
        }
        printf("\n");
    }
}

// Function to rotate the matrix 90 degrees clockwise
void rotate(int **M, const int size) {
    int i, j;
    int **temp;

    // Allocate memory for a temporary matrix
    temp = (int **)malloc(size * sizeof(int *));
    for (i = 0; i < size; i++) {
        temp[i] = (int *)malloc(size * sizeof(int));
    }

    // Copy the transpose of the matrix to the temporary matrix
    for (i = 0; i < size; i++) {
        for (j = 0; j < size; j++) {
            temp[i][j] = M[j][i];
        }
    }

    // Copy the rotated matrix back to the original matrix
    for (i = 0; i < size; i++) {
        for (j = 0; j < size; j++) {
            M[i][j] = temp[i][j];
        }
    }

    // Free the memory used by the temporary matrix
    for (i = 0; i < size; i++) {
        free(temp[i]);
    }
    free(temp);
}

// Function to check whether the matrix is symmetric
int symValid(const int **M, const int size) {
    int i, j;

    // Check if M[i][j] is equal to M[j][i] for all i and j
    for (i = 0; i < size; i++) {
        for (j = 0; j < size; j++) {
            if (M[i][j] != M[j][i]) {
                return 0; // Not symmetric
            }
        }
    }

    return 1; // Symmetric
}

// Function to perform matrix multiplication
int** mul(const int **M, const int size) {
    int i, j, k;
    int **result;

    // Allocate memory for the result matrix
    result = (int **)malloc(size * sizeof(int *));
    for (i = 0; i < size; i++) {
        result[i] = (int *)malloc(size * sizeof(int));
    }

    // Perform matrix multiplication
    for (i = 0; i < size; i++) {
        for (j = 0; j < size; j++) {
            result[i][j] = 0;
            for (k = 0; k < size; k++) {
                result[i][j] += M[i][k] * M[k][j];
            }
        }
    }

    return result;
}


int main() {
    int size;
    int **M, **Msq, **rotatedM;

    initialize(&M, &size);

    // Create a copy of the original matrix for rotation
    rotatedM = (int **)malloc(size * sizeof(int *));
    for (int i = 0; i < size; i++) {
        rotatedM[i] = (int *)malloc(size * sizeof(int));
        for (int j = 0; j < size; j++) {
            rotatedM[i][j] = M[i][j];
        }
    }

    // Rotate the matrix
    rotate(rotatedM, size);
    outputMatrix((const int **)rotatedM, size); // Cast to const int **

    if (symValid((const int **)rotatedM, size)) // Cast to const int **
        printf("Symmetric\n");
    else
        printf("Not symmetric\n");

    // Perform matrix multiplication using the original matrix
    Msq = mul((const int **)M, size); // Cast to const int **
    outputMatrix((const int **)Msq, size); // Cast to const int **

    // Free memory
    for (int i = 0; i < size; i++) {
        free(rotatedM[i]);
    }
    free(rotatedM);
    for (int i = 0; i < size; i++) {
        free(M[i]);
        free(Msq[i]);
    }
    free(M);
    free(Msq);

    return 0;
}
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