A binary operation x is defined by a x b = ab. If a x 2 = 2 – a, find the possible values of a?

A binary operation x is defined by a x b = ab. If a x 2 = 2 – a, find the possible values of a?
A. 1, -2
B. 2, -1
C. 2, -2
D. 1, -1

Correct Option: Answer is A
Solution:
a = b = a2
a + 2 = a2…..(i)
a + 2 = 2 – a…………..(ii)
a2 = 2 – a
a2+ a – 2 = a2 + a – 2 = 0
= (a + 2)(a – 1) = 0
a = 1 or – 2

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