var('a')
var('k')
A = matrix([[a,k,k],[k,a,k],[k,k,a]])
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"