A binary operation * is defined by a*b = ab. If a*2 = 2-a, find the possible values of a.

A binary operation * is defined by a*b = ab. If a*2 = 2-a, find the possible values of a.

Answer Details

a * b = ab
a * 2 = a2 = 2 - a
a2 + 2a - a - 2 = 0
a(a+2) - 1(a+2) = 0
(a-1)(a+2) = 0
a = 1, -2