[R] permutations from vectors out of a matrix

[Etienne Stockhausen]

Dear R-Users,
I'm relativley new to R and have the following problem. I need all 
permutations of the vectors created by the collumns of a matrix. I will 
give a small example:
   
    p=3
    
n=2^p-1                                                                         
#number of obtainable vectors
    mat=matrix(0,p,p)
    for(i in 1:p)
     {
       mat[i:1,i]=1/i
     }

mat is now a quadratic matrix and n is the number of the vectors I try 
to get when I compute all permutations of the vectors built by the 
individual columns. It should work for all quadratic matrix and I want 
to avoid using some 'special' packages.
In the example I need the following vectors at the end:
(1,0,0); (0,1,0); (0,0,1); (0.5,0.5,0); (0.5,0,0.5); (0,0.5,0.5); 
(1/3,1/3,1/3).
I hope my intention becomes clear.

I'm looking foward to any ideas and clues that might help me.
Thanks in advance and best regards.

Etienne