if A=B , is it the same to say B=A? if it's, then why? what's confusing me A=B isn't in writings the same B=A so how we determined that A=B is the same as B=A!!!!!
I know it's equal, but who said we just care on equal? maybe also on the order of writing the elements of two sides of equation .. who said not?!
Since another question hints that you know something about computer programming, it may be worth pointing out that
"=" can be used in different ways. Sometimes order doesn't matter, sometimes it does.
"Who says?" This is just an implicit agreement among users of the notation, in a particular context -- like all language! If you choose to be part of a community, and communicate with them, you use the words and symbols they use, in the way they use them.
In math, "=" by itself always means merely "is equal to". When we say that A = B, it means that quantities A and B are equal -- both quantities play the same role; it doesn't matter which order you put them. You can think of it as bidirectional, or symmetrical. (It can also be used in a definition, as in "let n = 3", which is not symmetrical; but even there, "=" just means these two quantities are equal; it is the sentence in which it is found that changes it from a mere statement of equality to a definition.)
This is what all mathematicians accept as the meaning. And this is what the symbol has meant since it was first invented, as described
here.
But some programming languages use "=" in a different way, meaning "is assigned", similar to the usage in definitions. There, writing A = B means "put the current value of variable B into variable A". This is one-directional; it actually tells the computer to do something to variable A, and not to B. For example, in programming you can say "x = x + 1", which in math would be nonsense, but in a program changes the value of x by adding 1 to it.
Similarly, in English, the word "is" can be used in different ways. Taking pka's example, "Samuel Clemens is Mark Twain" means that they are two names for the same person; but "Samuel Clemens is an author" describes one aspect of Clemens, and identifies only one of many people who are authors -- it doesn't equate
all that Samuel Clemens is with
all authors. Or, returning to math, we can say "a square is a rectangle" but "a rectangle is a square" means something very different; this usage is asymmetrical.
But many students think of "=" in math as if it meant "has the answer", as in "2 + 3 = 5" meaning "if you add 2 + 3, the answer you get is 5". That is a misunderstanding; it really means merely that 2 + 3 and 5 are two "names" for the same quantity. When you move from arithmetic into algebra, you have to leave that earlier way of thinking behind.