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  4. On R, binary operation * is defined by a * b=a+b+a b then identity and inverse of * are ...... respectively.

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Q. On $R$, binary operation $*$ is defined by $a * b=a+b+a b$ then identity and inverse of $*$ are ...... respectively.

Gujarat CETGujarat CET 2020

Solution:

If $a* e=e* a=a$ then $e$ is identity
$a+e+a e=a $
$e(1+a)=0$
$e=0 $ (identity)
Now if $a* b=e$ then $b$ is inverse of $a$
$a+b+a b=0$
$a=-b(1+a)$
inverse $b=\frac{-a}{1+a}$