>> n=3;
>> I=eye(n);
>> P=perms(1:n);
>> A=zeros(n^2,factorial(n));
>> for x=1:factorial(n)
t=I(:,P(x,:));
A(:,x)=t(:);
end
>> A

A =

     0     0     0     0     1     1
     0     0     1     1     0     0
     1     1     0     0     0     0
     0     1     0     1     0     0
     1     0     0     0     1     0
     0     0     1     0     0     1
     1     0     1     0     0     0
     0     1     0     0     0     1
     0     0     0     1     1     0

>> rank(A)

ans =

     5



>> n=4;
>> I=eye(n);
>> P=perms(1:n);
>> A=zeros(n^2,factorial(n));
>> for x=1:factorial(n)
t=I(:,P(x,:));
A(:,x)=t(:);
end
>> A

A =

  Columns 1 through 13 

     0     0     0     0     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0     0     0     1
     0     0     0     0     0     0     1     1     1     1     1     1     0
     1     1     1     1     1     1     0     0     0     0     0     0     0
     0     0     0     0     1     1     0     0     0     0     1     1     0
     0     0     1     1     0     0     0     0     1     1     0     0     0
     1     1     0     0     0     0     0     0     0     0     0     0     1
     0     0     0     0     0     0     1     1     0     0     0     0     0
     0     1     0     1     0     0     0     1     0     1     0     0     0
     1     0     0     0     1     0     1     0     0     0     1     0     0
     0     0     1     0     0     1     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     1     0     0     1     1
     1     0     1     0     0     0     1     0     1     0     0     0     1
     0     1     0     0     0     1     0     1     0     0     0     1     0
     0     0     0     1     1     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     1     1     0     0

  Columns 14 through 24 

     0     0     0     0     0     1     1     1     1     1     1
     1     1     1     1     1     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0     0
     0     0     0     1     1     0     0     0     0     0     0
     0     0     0     0     0     0     0     1     1     0     0
     1     0     0     0     0     1     1     0     0     0     0
     0     1     1     0     0     0     0     0     0     1     1
     1     0     1     0     0     0     0     0     0     0     0
     0     0     0     0     0     1     0     0     0     1     0
     0     1     0     0     1     0     0     1     0     0     1
     0     0     0     1     0     0     1     0     1     0     0
     0     1     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     1     0     0     0     1
     0     0     1     1     0     0     0     0     1     1     0
     1     0     0     0     1     1     0     1     0     0     0

>> rank(A)

ans =

    10




>> n=1

n =

     1

>> I=eye(n);
>> P=perms(1:n);
>> A=zeros(n^2,factorial(n));
>> for x=1:factorial(n)
t=I(:,P(x,:));
A(:,x)=t(:);
end
>> A

A =

     1

>> rank(A)

ans =

     1



>> n=2

n =

     2

>> I=eye(n);
>> P=perms(1:n);
>> A=zeros(n^2,factorial(n));
>> for x=1:factorial(n)
t=I(:,P(x,:));
A(:,x)=t(:);
end
>> A

A =

     0     1
     1     0
     1     0
     0     1

>> rank(A)

ans =

     2


>> n=5

n =

     5

>> I=eye(n);
>> P=perms(1:n);
>> A=zeros(n^2,factorial(n));
>> for x=1:factorial(n)
t=I(:,P(x,:));
A(:,x)=t(:);
end
>> rank(A)

ans =

    17