What does this have to do with linear algebra?

Mod, what? ? (Again finite I think)

Since they are isomorphic they certainly have the same number of elements.

Thus, , then certainly a weaker statement

What is ? The cyclic group?Deduce that C(subscript 3) * C(subscript 3) is not isomorphic to C(subscript 9)

Is it tru that C 3 * C 5 is isomorphic to C15

whats going on here!!?

You can just use the fundamental theorem,

Because they are distinct prime power decompositions.

Because .