How to find all the linear transformations from $X$ to $X$?

90 Views Asked by At

I am considering the space of $mod~2$ space, e.g., 1+1=0.

If $X=\left\{ (0,0), (1,0), (0,1), (1,1) \right\}$, how can I find all the linear transformations from $X$ to $X$?

Do I have to check all $4^4=256$ functions, one by one?