Q63 / 180 · COMEDK 2017 · Mathematics

If $*$ be a binary operation on a set $A$ and $e$ be the identity element w.r.t. *, then $b \in A$ is said to be inverse of $a \in A$ w.r.t. * , if

  • A
    $a^{*} e=b^{*} e$
  • B
    $a=b$
  • C
    $a * a=b * b$
  • Correct answer
    D
    $a * b=b * a=e$

Solution

$b \in A$ is said to be an inverse of a w.r.t. operation $*$ if $a * b=b * a=e$. [by definition]

Hence, the correct answer is option: 'D'.

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