Two reasons to install an inverter. The first is because you have low-power or essential appliances that have no low voltage capability (or you don't want to buy the 12V adapter), and you would be using the power anyway - e.g. a Laptop, Samsung inverter fridge, CPAP machine. No real down sides of doing this.
The other reason is you want use a 240 plug to supply high power devices like coffee machines an toasters and microwaves. This can be done, but the issue is not installing the inverter, its working out size requirements and installing the batteries and solar needed to supply the inverter.
For a more detailed and useful answer we would need to know why you are considering it and maybe a bit more about your current setup.