A binary operation * is defined over the set B can be represented on a square table as follows;

                     Set B = {a, b, c}

Order of a group; this is just the number of element in the set.

 Example;

An operation * is defined on the set of multiplication, where S = {1, 3, 5, 7, 9} in mod 10

1. draw an operation table for the set S under *
2. state whether the set forms a group or not
3. state the order of the group

solution;

• the operation is closed since no element is added
• (1*3) *5= 1* (3*5) [locate in diagram]

3*5 = 1*5

5 = 5 hence associative

• From operation above, identity element e = 1, because at “1” the set repeats vertically and horizontally
• The inverse of an element is gotten where the identity element is found in the set of operation (painted in yellow above), that is;

Hence the operation has no inverse since not complete. And therefore doesn’t form a group

1. The order of the operation = 5