Question

Luke says you can always add and always multiply to join groups. Is he correct?

Answer 1

Suppose G is a finite group having elements natural numbers.

→→→  If you add any two members of the group, you will get member of the group,because a group satisfy closure property with respect to addition.

For example, 2 ∈N,3∈N→2+3=5∈N

→→Similarly, if you multiply any two members of the group, you will get member of the group,because a group satisfy closure property with respect to multiplication.

  For example,: 2 ∈N,3∈N→2×3=6∈N

Yes, He is Correct.

Answer 2

Yes, because only equal groups can be multiplied