Composition of Matrix relation

I am unsure if this exercise is possible to do, could anyone tell me if I am correct or not?

We have DOMAIN {1, 2, 3} and RANGE {1, 2, 3, 4} and relation R = {(1, 2), (2, 3), (3, 4)}

The exercise say to find R^2.

I have tried two way to find this.

1. Matrix composition. Here i cam across the problem that you cannot compose a 3x4 matrix with another 3x4

2. Compose the relations themselves what i get is {(1,3) ,(2,4) , (3,?)}

I cant see how i can find the 4 to replace ?

Interpretation 2 is correct (interpretation 1 is not). According to the prescription for $R$, $$ 1\mapsto2\,,~~2\mapsto3\,,~~3\mapsto4\,. $$ Then, if we compose $R$ with itself, we get$$ 1\mapsto2\mapsto3\,,~~2\mapsto3\mapsto4\,,~~3\mapsto4\mapsto\mbox{(nothing)}\,. $$ That is, in the last spot, since 4 is not in the domain of $R$, we can't plug 3 into $R^2$. Thus, 3 is not in the domain of $R^2$, and the relation $R^2$ is defined by the prescription $$ R^2:1\mapsto3\,,~~2\mapsto4\,. $$ In the language of ordered pairs, $$ R^2=\{(1,3),(2,4)\}\,. $$ The domain is the set $\{1,2\}$, and the range is the set $\{3,4\}$.