matrices - Lights Out with custom rules set

I'm trying to understand how to use linear algebra to solve a custom Lights Out puzzle with the following rules:

There are 8 lights, all the lights are off at the starting point, I need to turn on all of them.
Every button change (on\off) of the lights like that:
(If the light was on, it will turn it off, if it was off, it will turn it on)

1 1 0 1 1 0 0 0

1 1 1 1 0 0 1 1
0 1 1 0 0 0 0 1
1 1 0 1 1 1 1 0
1 0 0 1 1 1 0 0
0 0 0 1 1 1 1 0
0 1 0 1 0 1 1 0
0 1 1 0 0 0 1 1

For example:

Button 1 will change lights 1, 2, 4 and 5

Button 2 will change lights 1, 2, 3, 4, 7 and 8
You got the idea...

We start with

0 0 0 0 0 0 0 0

And we need to get to

1 1 1 1 1 1 1 1

I got no idea how to even start, I tried to solve it with many matrix but I didn't really understand what I was doing, so I failed. Any help will be appreciated.