JAMB 1992 · UME · Q21

Binary operations

If the binary operation $*$ is defined by $m * n = mn + m + n$ for any real numbers $m$ and $n$ , find the identity element under this operation.

Worked solution (try it first)

The identity $e$ leaves every $m$ unchanged: $m * e = m$ for all $m$ .
Use the rule: $me + m + e = m$ .
Take $m$ from both sides: $me + e = 0$ , so $e(m + 1) = 0$ .
This must hold for every $m$ , so $e = 0$ , option D.

Report a problem with this question