Search any question & find its solution
Question:
Answered & Verified by Expert
If $Q_{1}$ is the set of all relations other than $1$ with the binary operation * defined by $a * b=a+b-a b$ for all $a, b$ in $Q_{1}$, then the identity in $Q_{1}$ with respect to $*$ is
Options:
Solution:
1771 Upvotes
Verified Answer
The correct answer is:
$0$
Let $e$ be the identity element, then
$a$ * $\boldsymbol{e}=a$
$\Rightarrow \quad a+e-a e=a$
$\Rightarrow \quad e(1-a)=0$
$\Rightarrow \quad e=0 \quad[a \neq 1]$
$a$ * $\boldsymbol{e}=a$
$\Rightarrow \quad a+e-a e=a$
$\Rightarrow \quad e(1-a)=0$
$\Rightarrow \quad e=0 \quad[a \neq 1]$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.