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

Answer 1

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.