Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry?

I believe the homogeneous Maxwell equations obey parity and time reversal symmetry separately - is that right? The homogeneous Maxwell equations reduce to a wave equation in which space and time appear as second order derivatives.

Here's my effort at answering my first question.

In the first inhomogeneous equations one has:

$$\mathbf{\nabla . E} = \frac{\rho}{\epsilon_0}$$

If I change the sign of x,y,z, in $\mathbf{\nabla . E}$ then I must change the sign of $\rho$ to balance it.

In the third equation one has:

$$ \mathbf{\nabla \times E} = - \frac{\partial \mathbf{B}}{\partial t}$$

As the sign of x,y,z has changed then the sign of t must change to balance it.

Thus we must have CPT symmetry. This can be checked in the last equation:

$$\mathbf{\nabla \times B} = \mu_0 \mathbf{j} + \frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$$

The sign of x,y,z in $\mathbf{\nabla \times B}$ has changed. This is balanced by a sign change of t in $\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$. The sign of $\mathbf{j}$ has changed because the charge has changed sign.

Thus the inhomogeneous Maxwell equations obey CPT symmetry rather than C,P or T alone.

Is this reasoning right?