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
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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.
Source: Myschool Past Questions Archive (Record #30713)