In order to deduct my home office expenses, do I need to be able to prove anything?

It should be written into your employment contract that you work from home as a condition of your work, or if you mostly earn commission from your employer then you can claim home office expenses as well.

The important thing is to make sure you have a "dedicated" office to work from. For the actual deduction, you would need to measure out the area in your home as a percentage of the overall premises and use this as your apportionment for any related expenses