Question

what is the total resistance across A and B in the circuit

Answer 1

it's a case of balanced Wheatstone bridge...

so, you can eliminate centre resistor of 2 ohm...

Now, upper two resistors as well as lower two resistors of 2 ohm become series combination and again those two combinations come into a parallel combination.

so, resultant resistance :

2 ohm and 2 ohm in series give 4 ohm.
again lower 2 ohm and 2 ohm in series give 4 ohm..

now, these 4 ohm and 4 ohm in parallel give 2 ohm resistance..

hence resultant resistance of the combination = 2 ohm