Generating Permutation Matrices in Octave / Matlab

I have been doing Gilbert Strang’s linear algebra assignments, some of which require you to write short scripts in MatLab, though I use GNU Octave (which is kind of like a free MatLab). I was trying out this problem:

To solve this quickly, it would have been nice to have a function that would give a list of permutation matrices for every n-sized square matrix, but there was none in Octave, so I wrote a function permMatrices which creates a list of permutation matrices for a square matrix of size n.

	% function to generate permutation matrices given the size of the desired permutation matrices
	function x = permMatrices(n)
	x = zeros(n,n,factorial(n));
	permutations = perms(1:n);
	for i = 1:size(x,3)
	x(:,:,i) = eye(n)(permutations(i,:),:);
	end
	endfunction

view raw permMatrices.m hosted with ❤ by GitHub

For example:

The MatLab / Octave code to solve this problem is shown below:

	% Solution for part (a)
	p = permMatrices(3);
	n = size(p,3); % number of permutation matrices
	v = zeros(n,1); % vector of zeros with dimension equalling number of permutation matrices
	% check for permutation matrices other than identity matrix with 3rd power equalling identity matrix
	for i = 1:n
	if p(:,:,i)^3 == eye(3)
	v(i,1) = 1;
	end
	end
	v(1,1) = 0; % exclude identity matrix
	ans1 = p(:,:,v == 1)

	% Solution for part (b)
	P = permMatrices(4);
	m = size(P,3); % number of permutation matrices
	t = zeros(m,1); % vector of zeros with dimension equalling number of permutation matrices
	% check for permutation matrices with 4th power equalling identity matrix
	for i = 1:m
	if P(:,:,i)^4 == eye(4)
	t(i,1) = 1;
	end
	end
	% print the permutation matrices
	ans2 = P(:,:,t == 0)