WAEC 2023 · Paper 1 · Q32

The table shows the operation $*$ on the set $\{x, y, z, w\}$ .

Find the identity element.

Worked solution (try it first)

The identity $e$ leaves every element unchanged: $e * a = a$ and $a * e = a$ .
The row for $z$ reads $x, y, z, w$ , the same as the top row, so $z * a = a$ .
The column for $z$ reads $x, y, z, w$ , the same as the left column, so $a * z = a$ .
So the identity element is $z$ , option C.