A binary operation * defined on the set S= {a,b,c} is presented in the following Cayley’s table.*abcaabcbbcaccabShow that (S,*) forms a group.
From the table,
We see that the operation defined on any two elements of S gives an element of S itself.
i.e. For each a,b S, a*b = S
So, S is closed under operation *.
For each a,b S,
a * (b * c) = (a * b) * c
or, a * a = b * c
or, a = a (true)
So, * satisfies associative property.
a * a = a,
a * b = b * a= b
and, a * c = c * a = c
a is an identity element.
a * a = a,
a is the inverse of a.
Similarly, b * c = c * b = a,
b and c are the inverse...