make an r by m permutation matrix

I have the following code :

A = eye(r);
L = [];
for i = 1:10
    A = A(randperm(r),:);
    L = [L A]; % 10 x 100 matrix with only one nonzero entry per column
end

The variable L is a 10x 100 size matrix. however i want to make a more intelligent code such that,

the dimensions will depend on the dimension of an input data matrix. for example when i input X, i.e.

% r is my rank. m and n are the dimensions.
X = rand(m,r)* rand(r,n);

% I want L to have dimension of [m by r] or [r by n] .
%  i.e. it should pick on of the sides of X and the other side r