算出来A*A不等与A^2...求教

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cstdlib>
#define n 2
using namespace std;
struct matrix {
    int x[n+1][n+1];
    matrix() {
        memset(x,0,sizeof(x));
    }
    void fill(int q) {
        int maxx=sizeof(x)/sizeof(int);
        int* p=&x[0][0];
        while(maxx>0) {
            *p=q;
            p++;
            maxx--;
        }
    }
};
matrix operator *(matrix a,matrix b)
{
    matrix ans;
    ans.fill(0);
    for(int i=1; i<=n; i++) {
        for(int j=1; j<=n; j++) {
            for(int k=1; k<=n; k++) {
                ans.x[i][j]+=a.x[i][k]*b.x[k][j];
            }
        }
    }
    return ans;
}

matrix operator ^(matrix a,int b)
{
    matrix base=a,ans;
    ans.fill(1);
    while(b) {
        if((b&1)!=0) {
            ans=ans*base;
        }
        base=base*base;
        b>>=1;
    }
    return ans;
}

void matrixinput(matrix& a)
{
    for(int i=1; i<=n; i++) {
        for(int j=1; j<=n; j++) {
            cin>>a.x[i][j];
        }
    }
}

void matrixoutput(matrix& a)
{
    for(int i=1; i<=n; i++) {
        for(int j=1; j<=n; j++) {
            cout.width(5);
            cout<<a.x[i][j];
        }
        cout<<endl;
    }
}

int main()
{
    matrix a,b,c;
    cout<<"input A"<<endl;
    matrixinput(a);
    cout<<"input B"<<endl;
    matrixinput(b);
    cout<<"answer of A*B"<<endl;
    c=a*b;
    matrixoutput(c);
    int d;
    c.fill(1);
    cout<<"input power"<<endl;
    cin>>d;
    c=a^d;
    cout<<"answer of A^d"<<endl;
    matrixoutput(c);
}