optimization problem of a random process

I have a random matrix A=rand(3,3); I have an operation F= Transpose(A)xAxG

Problem is that A is not known before hand. I just know only the output of the operation and input.

My aim is to find a G such that A*G= [0 0 0; 0 1 0; 0 0 0].

My initial G=rand(3,3). please any one have any idea how can i do that ?

[Torsten]

Description of the problem is unclear (at least for me).

Best wishes

Torsten.