Generate random permutation matrix

I am trying to generate a random square matrix A of dimension n that has one and only one 1 per row and column. My idea is the following, but as a result I get a matrix of all 1s. What am I doing wrong?

 A = zeros(n);
 p = randperm(n);
 x = 1:n;
 p = p';
 x = x';
 A(p,x) = 1;

Answer 1

[James Tursa]

Another way:

A = eye(n);
A = A(randperm(n),:);

Answer 2

[Star Strider]

See if this does what you want:

n = 5;                                                  % Set Matrix Size
p = randi([2 n], n);                                    % Create Matrix EXCLUDING ‘1’
x1 = sub2ind(size(p), randperm(n), randperm(n));        % Create Linear Indices For ‘1’
p(x1) = 1;                                              % Put ‘1’ Randomly In Each Row, Column

Experiment to get the result you want.