Linear algebra – System – Trivial and non-trivial solutions

So I have a system like this:

x + (2p - 1) and - pz = 0
(2 - p) x + y - z = 0
x + py - z = 0

and the questions are:

  • For what values ​​of p, does the system have trivial solutions?
  • For what values ​​of p, the system has non-trivial solutions? Write them

Now I have arrived at p1 = 1, p2 = 1, p3 = 1/2 with the Sarrus rule. Now, how do I get trivial and non-trivial solutions? I'm just looking for instructions