Is it allowed to ground the negative pole of a sine wave inverter?

I have an off-grid PV system and somehow there's no connection to the earth on my inverter. This creates certain problems with the touchpad when using my notebook. The mouse pointer jumps back and forth at random.

I bought a grounding rod and sunk it next to the garden shed and connected a 10qmm green-yellow cable to it.

Can I now also connect this cable to the negative pole of the inverter? The inverter has a metal housing but unfortunately no connection for grounding.

You should earth the metal housing of an inverter (but it is usually internally connected to the protective conductor and therefore earthed).

The DC voltage of the PV panel and battery is not grounded (neither + nor -)

Usually, however, there's also a clear indication on the inverter that the panel / battery voltage must not be grounded.

On the DC side, you must not earth the system because of the galvanic separation. The panels or the bracket should have an earth connection, but this is "only" lightning protection and has nothing to do with your problem. What kind of system is that? Grid-related (i.e. With feed into the grid) or purely for self-supply (e.g. Garden shed). With memory?

I bought the inverter used. Unfortunately there's no manual for this. I was just curious how the experts here will answer my question.

First of all, thanks for the star.

In the case of transformerless inverters, there are also some exceptions where the DC voltage may be grounded (e.g. Some devices from Sunways or Omron, possibly others as well), but it is also important for these manufacturers whether the device is actually designed for this, exact type and, if necessary, inquire with the manufacturer if the PV side is to be earthed.