Hello,
Some things to remember are these:
1. A voltage source E in series with a resistance R is the same as a current source
in parallel to that same resistance R, with the current source equal to E/R.
2. A current source I in parallel to a resistance R is the same as a voltage source
in series with that same resistance R, where the voltage source is equal to I*R.
Using (1) with the voltage source in the circuit, we get a current source in
parallel to a resistance R, and when that R is in parallel to the center resistance
we get 1 ohm, but more importantly the new current source is equal to E/R
which equals exactly 2 amps, which happens to equal the original current source,
so the current at the top central node flows in and flows out through the
original current source leaving no current to flow through the center resistance
which means 0v at the central node. The result anyway is a 2 amp current
flowing through a 2 ohm resistor which means the voltage A to B is 4 volts,
and since a current source has infinite impedance the output resistance is
2 ohms. You can test this by theoretically injecting a small perturbation current
I into the output and noting how the output voltage changes. For example,
injecting 1ma forces the voltage to step up to 4.002v, where it originally was 4.000v,
and 0.002/0.001 is equal to 2 ohms.