var('x')
A = matrix([[1,0,0],[0,cos(x),-sin(x)],[0,sin(x),cos(x)]])
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"