Let M be a matrix:

M =
|m1 m2|
|m3 m4|

What are the minimum necessary conditions that M must fulfill so that there exists another matrix P (P =/= M(^-1)) such that:

MP + PM = 2I (where I is the identity matrix).

I suspect that the answer is m1 = -m4, but I can't find a way to prove it. Any help or pointers, anybody?