Did I do the composition of $R_1$ and $R_2$ properly?

Question

I've been learning about compositions of relations. I was wondering if someone can critique my work to see if I've done it right.

Given a set $A = \{a,b,c,d\}$

Given $R_1 = \{ (a,b), (a,c), (d,d) \}$

Given $R_2 = \{ (a,c), (b,a), (b,c), (b,d), (d,c) \}$

Find $ R_1 \circ R_2 $ and $ R_2 \circ R_1 $

My working:

$$\begin{align} R_1 \circ R_2 &= \{ (b,b), (b,c), (b,d) \} \\ R_2 \circ R_1 &= \{ (a,a), (a,c), (a,d), (d,c) \}\end{align}$$

Answer 1

Both of your answers are correct.