||'''Book'''|| Advanced Engineering Mathematics ||
 ||'''Author'''|| Erwin Kreyszig ||
 ||'''Edition'''|| 8th Edition ||

/* code_begins */

{{{
A = matrix([[ -3, 1, 5],[ 1, 0, -2],[ 5, -2, 4]])
print A
print "Is symmetric?", A.is_symmetric() 
print "Is skew_symmetric?", A.is_skew_symmetric() 
print A.transpose()==A.inverse()
if(A.transpose()==A.inverse()):
    print this is orthogonal
else:
    print "this is not orthogonal"
B = matrix([[ 0, 9, -12],[ -9, 0, 20],[ 12, -20, 0]])
print B
print "Is symmetric?", B.is_symmetric() 
print "Is skew_symmetric?", B.is_skew_symmetric() 
print "this is not orthogonal"
C = matrix([[ 2/3, 1/3, 2/3],[ -2/3, 2/3, 1/3],[ 1/3, 2/3, -2/3]])
print C
print "Is symmetric?", C.is_symmetric() 
print "Is skew_symmetric?", C.is_skew_symmetric() 
print C.transpose()==C.inverse()
if(C.transpose()==C.inverse()):
    print "this is orthogonal"
else:
    print "this is not orthogonal"
}}}

/* code_ends */

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