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+//page 304
+//Example 8.27
+clc;
+clear;
+close;
+disp('Unitary and orthogonal matrices');
+//part a
+disp('A = ');
+disp('[c]');
+disp('A is orthogonal if c = +1 or -1');
+disp('A is unitary if absolute value of c is 1, i.e. |c| = 1');
+disp('-------------------------------------------------');
+//part b
+disp('A = ');
+disp('a    b');
+disp('c    d');
+disp('A is orthogonal if, ');
+disp('A'' = inv(A)');
+disp('inv(A) = 1/(ad - bc) * X');
+disp('where X = ');
+disp(' d    -b');
+disp('-c     a');
+disp('Determinant of orthogonal matrices is +1 or -1');
+disp('So A is orthogonal if,');
+disp(' a   b');
+disp('-b   a');
+disp('or');
+disp('a    b');
+disp('b   -a');
+disp('where, a^2 + b^2 = 1');
+//part d
+disp('A is unitary if,');
+disp('A'' = inv(A)');
+disp('inv(A) = 1/(ad - bc) * X');
+disp('where X = ');
+disp(' d    -b');
+disp('-c     a');
+disp('Determinant of unitary matrices is +1 or -1');
+disp('So, A is unitary if,');
+disp('A = ');
+disp('a                                b');
+disp('-(e^i*x)*b_bar       (e^i*x)*a_bar');
+disp('A = ');
+disp('1    0                *            a         b');
+disp('0    e^(i*x)                    -b_bar     a_bar');
+disp('where x ia real number, and a,b are complex nos.');
+disp('|a|^2 + |b|^2 = 1');
+disp('-----------------------------------');
+//part c
+disp('A = ');
+disp('cos(thetha)         -sin(thetha)');
+disp('sin(thetha)          cos(thetha)');
+disp('A is orthogonal.');
+disp('If thetha is real, then A is unitary.');
+//end