If (Z, ∗) is a group with a ∗ b = a + b + 1, ∀a, b ∈ Z. The inverse of a is?
- -a -2
- a - 2
- -2
- None of these
Explanation
Given the operation a * b = a + b + 1:
Let's find the identity element 'e' such that a * e = a.
a * e = a + e + 1 = a
This implies e + 1 = 0, so e = -1.
Now, to find the inverse 'x' of 'a' such that a * x = e = -1:
a * x = a + x + 1 = -1
This implies a + x = -2.
x = -2 - a
x = -a - 2
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