  Time reversal symmetry is studied in a space with noncommutativity of
coordinates and noncommutativity of momenta of canonical type. The circular
motion is examined as an apparent example of time reversal symmetry breaking in
the space. On the basis of exact solution of the problem we show that because
of noncommutativity the period of the circular motion depends on its direction.
We propose the way to recover the time reversal and rotational symmetries in
noncommutative phase space of canonical type. Namely, on the basis of idea of
generalization of parameters of noncommutativity to tensors we construct
noncommutative algebra which is rotationally-invariant, invariant under time
reversal, besides it is equivalent to noncommutative algebra of canonical type.
