### How to enumerate the generalised inverse of given matrix?

Let $A$ be a given singular matrix over a finite field. Then how to enumerate the solutions of the system of equation

$$Ax=b, b \in R(A), \text{range of } A $$

Since, $A$ is singular matrix I can find the generalized inverse $G$ (i.e., AGA=A) of $A$ . Note that, $Gb$ is one of the solution. And so the set of all solution can be written as
$${Gb+(I-GA)u: u \text{ is arbitrary }}$$

Now, how to incorporate these ideas in sagemath?

I am a newbie to sagemath. So, the answerers kindly give me with the details.

Thanks in advance.