I am a beginner in C++ .i wrote this code in which operator is overloaded on matrices.Go thru the program;

When i compile the above prog i get an error :Code:: /*prog.cpp*/ #include<iostream.h> #include<conio.h> int k=1; class matrix { private: static int a[20][20]; int m,n; public: friend istream& operator>>(istream &cin,matrix&); friend ostream& operator<<(ostream &cout,matrix); friend matrix operator+(matrix,matrix); friend matrix operator-(matrix,matrix); friend matrix operator*(matrix,matrix); friend matrix operator/(matrix,matrix); }; istream& operator>>(istream &cin,matrix &a) { int i,j; cout<<"Enter the size of the matrix m,n"<<endl; cin>>a.m>>a.n; cout<<"Enter the matrix"<<endl; for(i=0;i<=a.m-1;i++) for(j=0;j<=a.n-1;j++) cin>>a.a[i][j]; return(cin); } ostream& operator<<(ostream &cout,matrix a) { int i,j; cout<<"The matrix is as follows"<<endl; for(i=0;i<=a.m-1;i++) { for(j=0;j<=a.n-1;j++) cout<<a.a[i][j]<<"\t"; cout<<"\n"; } return(cout); } matrix operator+(matrix a,matrix b) { matrix c; int i,j; c.m=a.m; c.n=a.n; for(i=0;i<=a.m-1;i++) for(j=0;j<=a.n-1;j++) c.a[i][j]=a.a[i][j]+b.a[i][j]; return(c); } matrix operator-(matrix a,matrix b) { matrix c; int i,j; c.m=a.m; c.n=a.n; for(i=0;i<=a.m-1;i++) for(j=0;j<=a.n-1;j++) c.a[i][j]=a.a[i][j]-b.a[i][j]; return(c); } matrix operator*(matrix a,matrix b) { matrix c; int i,j; c.m=a.m; c.n=b.n; if(a.n==b.m) { for(i=0;i<=a.m-1;i++) for(j=0;j<=b.n-1;j++) for(k=0;k<=a.n-1;k++) c.a[i][j]+=a.a[i][k]+b.a[k][j]; } else k=0; return(c); } matrix operator/(matrix a,matrix b) { matrix c; int i,j; c.m=a.m; c.n=a.n; for(i=0;i<=a.m-1;i++) for(j=0;j<=a.n-1;j++) c.a[i][j]=(float)a.a[i][j]/float(b.a[i][j]); return(c); } main() { matrix a,b,c,d,e,f; cin>>a>>b; c=a+b; d=a-b; e=a*b; f=a/b; cout<<"The addition of matrices is:"<<"\n"<<c; cout<<"The subtraction of matrices is:"<<"\n"<<d; if(k==1) cout<<"The multiplication of matrices is:"<<"\n"<<e; else cout<<"The multiplication of matrices is not possible"<<endl; cout<<"The division of matrices is:"<<"\n"<<f; getch(); return(0); }

"Linker error:undefined symbol matrix::a in module prog.cpp"

please help me out with the error.