Question
Mark the correct alternative in the following question for the binary operation * on Z defined by a * b = a + b + 1, the identity element is:
- 0
- -1
- 1
- 2
✓
Answer
- -1
We have,
a * b = a + b + 1
Let e be the identity element of *. Then,
a * e = a = e * a
a + e + 1 = a
e = a - a - 1
e = -1
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