Let * be a binary operation on Z defined by a * b=a+b−15 . The inverse of element 21 in Z, ) is

Question

Let * be a binary operation on $Z$ defined by $a$ * $b=a+b-15$ for $a, b \in Z$. The inverse of element 21 in $(Z$, ) is

(A) 12

(B) -21

(C) 9

(D) $1 / 21$

Answer 1

Let $a \in Z$ and $b$ be its inverse

$\therefore a^* b=e=b^* a \\$

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

$\Rightarrow b=30-a \in Z \\$

$\therefore \text { The inverse of } a \in Z \text { is } 30-a$

$\mathrm{a}^* \mathrm{~b}=2^{5 \mathrm{ab}} ; \mathrm{a}, \mathrm{b} \in \mathrm{N}$