Question

Juan says, "When you put together unequal groups, you can only add." Is he correct? Explain.

Answer 1

Yes, Juan is correct only equal groups can be multiplied.

Answer 2

Consider two groups

A = {1,w,w²}, Identity element =1

And, B= {1,-1}Identity element =1

Both are forming groups with respect to multiplication.

The first group A has 3 elements and the second group B has 2 elements.

Do, you think can we add them.

How will you add them, there are three elements in group A and 2 elements in group B, giving no benefit.

No, we can't add them.