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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 ________________ .
Options
0
-1
1
2
Solution
We have,
a * b = a + b + 1
Let e be the identity element of *. Then,
\[a * e = a = e * a\]
\[ \Rightarrow a + e + 1 = a\]
\[ \Rightarrow e = a - a - 1\]
\[ \therefore e = - 1\]
Hence, The identity element is -1.
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