How to find reflexive, symmetric and transitive closure of a relation R?

Question

I have to solve this question. Any hints or what closure actually means?

Let $R = \{(1,2),\ (2,3),\ (3,1)\}$ and $A = \{1,2,3\}$. Find the reflexive, symmetric, and transitive closure of $R$ using

1. composition of relation $R$,
2. composition of matrix relation $R$, and
3. graphical representation of $R$.

Answer 1

HINT: I give you just the reflexive closure with (i), hoping you will do what remains.

1R2 & 2R3 & 3R1 implies 1R1.

2R3 & 3R1 & 1R2 implies 2R2

3R1 & 1R2 & 2R3 implies 3R3