Question

Let * be a binary operation on $Z$ defined by $a{ }^* b=a+b-15$ for $a, b \in Z$. The identity element in $(Z$, ) is

(A) 5

(B) 10

(C) 15

(D) 0

Answer 1

SOLUTION : Let $\mathrm{e}$ be the identity element.

$\therefore \text { For } a \in Z, \quad a^* e=a=e^* a \\$

$\Rightarrow a+e-15=a=e+a-15 \\$

$\Rightarrow e-15=0 \Rightarrow e=15 \in Z \\$

$\therefore \text { The identity element is } 15 .$

Above Correct Answer is Option C.