Solution to Problem 13, Section 2.7 Linear Algebra (Gilbert Strang)

Section2_7_13.m

% 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)