So - A && B == B && A ?
Not according to my mother. She seems to think that "eat the rice and I'll give you dessert" is different from "give me dessert and I'll eat the rice"

If you don't eat that rice, you'll eat nothing at all! You have five minutes!

Asynchronous much? We live in a post-truth era so you can use that as an argument right there...

No, your situation is A => B == B => A, which is not true

Something wrong with your rice?

From the computer's point of view, A && B != B && A.
When it checks A && B, if A is already false, then it has no reason to check B anymore, and if B is a function it will not be run. Vice versa.

Example (Java):
String X = null;
// A: X != null
// B: X.equals("Something")

// A && B
X != null && X.equals("Something")
/* Returns false because A is false, no more need to evaluate and check B. */

// B && A
X.equals("Something") && X != null
/* NullPointerException because a method cannot be executed on null. */

@leduyquang753 nice, but not true for all languages (PHP, I think, for example)

@DustInCompetent no chocolate

from a parents point of view it is more like
A && B != B || A
because more often than not it's becomes the procession of the second part where A doesn't matter if B was true already.

@erroronline1 so maybe B^A (xor)

Logic applied to life == realisation that life is an illogical mess governed by laws of logic for some reason. Go figure

@jnfsmile php does the same, i had this dilemma recently