How to get certain value from matrix multiplication?

Hello everyone, sorry if this is a basic question. I have two matrix

a = [1     0     0     1]

and

b = [1     0     1     1     0     0     0
     1     1     0     0     0     0     1
     0     0     1     0     1     1     0
     1     0     0     0     1     0     1]

I multiply these two using modulo operation, so it will become

c = [0     0     1     1     1     0     1]

What i want to ask is, is it possible to get the exact value of a if have the c first? Something like a reverse operation to find a from c, but i don't know what to do with b. If it is possible, how is the correct way to do that? Thank you.

[James Tursa]

If c is the result of modulo(a*b,2) then there might not be a unique solution. I.e., there might be multiple different a's that would work. How do you plan to deal with that? Or is any a that works acceptable? How large can the dimensions of everything be?

Answer 1

[Torsten]

https://de.mathworks.com/help/comm/ref/gflineq.html