Help with a Multiple Choice "Function" type Problem

[M98Ranger]

From GRE PP Practice Test 1

The operation & is defined for real numbers only. X&Y=X^2+Y^2-X*Y. Which of the answer choices is NOT true?

(A) X&X = x^2
(B) X&Y = Y&X
(C) X&1 = x (Correct Answer)
(D) X&0 = x^2
(E) X&Y = (-X)&(-Y)

What is the quickest way to come to the answer. Thoughts about efficient ways of solving this would be appreciated.

[buckykatt]

I'd approach this by just performing each operation on the left hand side and checking the answer against the right hand side until I found one that didn't match. On average, you'd only have to check 2.8 (since, if the first four were true, you wouldn't have to check the fifth). Though, careful person that I am, I'd probably check all five anyway.

[KBTA]

Calculcation by inspection is the fastest way I think.
This is almost (a-b)^2 formula. Here product term is ab instead of 2ab "&" is working as "-" sign .

[M98Ranger]

Alright thats what I thought, but I wasn't sure. Thanks for the advise!