JAMB 1998 · UME · Q21

Binary operations

The identity element with respect to the multiplication shown in the table is

$\otimes$	$p$	$q$	$r$	$s$
$p$	$r$	$p$	$r$	$p$
$q$	$p$	$q$	$r$	$s$
$r$	$r$	$r$	$r$	$r$
$s$	$q$	$s$	$r$	$q$

Worked solution (try it first)

The identity $e$ leaves every element unchanged, so its row and its column must repeat the headings $p, q, r, s$ .
The row for $q$ reads $p, q, r, s$ , and so does the column under $q$ .
So the identity is $q$ , option B.

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