Let (z, *) is a group with x*y=x+y-2 then inverse of x is ___________
Let (z, *) is a group with x*y=x+y-2 then inverse of x is ___________ Correct Answer -(x+4)
Let, Identity element I, x*I = I*x = x ⇒ x = x + I – 2 ⇒ I = 2. Inverse of x is x-1 Now, x*x-1 = I ⇒ x + x-1 – 2 = 2 ⇒ x-1 = -(x+4).
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Feb 20, 2025