The identity element with respect to the multiplication shown in the diagram below is \(\begin{array}{c|c} \otimes & p & p & r & s \\ \hline p & r & p & r & p
\\ q & p & q & r & s\\ r & r & r & r & r\\ s & q & s & r & q\end{array}\)

A.

p

B.

q

C.

r

D.

s

Correct answer is B

The identity element (e) under an operation, say \(\otimes\), is the element such that for any given element under the operation, say a,

\(a \otimes e = e \otimes a = a\)

From the table, q is the identity element.

\(p \otimes q = q \otimes p = p\)

Same as all through.