Commuting with the matriciant does not imply commuting with the integral

For time-varying linear systems with piecewise continuous coefficients the property of the system matrix to commute with the matriciant is shown not to require commuting with the integral. Commuting with the integral yields the possibility of matriciant representation as the exponential of the integral (Brockett) and therefore commuting with the matriciant. We show that the converse result does not hold in the class of piecewise continuous matrices. The relationship with the peaking in the systems stabilized by state feedback and by output injection is discussed