how to setup matrix with random unique combinations

Hello, in a M = 4x4 matrix I want to place 1 unique value (x=1) per column so that sum(M,2) = 1: e.g., [1 0 0 0; 0 0 0 1; 0 1 0 0; 0 0 1 0 ]

However the combination has to be randomly made.

I can use randi(4,1) to set up the first column, but the subsequent columns will have to be constrained following the first column and using "while" doesn't seem to help. Sugestions?

Answer 1

[Fangjun Jiang]

a=eye(4);
b=randperm(4);
c=a(b,:)

[Pablo]

Thank you, this works well!

Answer 2

[Laura Proctor]

If the columns and rows must all sum to 1, then try this:

M = eye(4);
M = M(:,randperm(4));