Does the following association multiplication table defined

Does the following association multiplication table defined on the set G={a,b,c,d} form a group? Support your answer

o

a

b

c

d

a

a

c

d

a

b

b

b

c

d

c

c

d

a

b

d

d

a

b

c

Solution

yes it does

Reason   -: In this example, a is the identity, and b and c are mutually inverse to each other.
A group is called abelian if it satis es the commutative law

this is the only possible way we could the table given the condition that a is the
identity. If we chose b to be identity and rearrange the heading column so that the identity is the
rst element of the heading column or row. Hence it does.