Matrices- Is this relationship transitive?

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Let $Z$ be the set $\{1,2,3\}$ Then the relation $R: \{(1,1) (2,2) (3,3) (3,1) (3,2) (1,3) (1,2)\}$ is transitive? How to represent matrix?

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Yes, it is transitive.

The usual way to represent the relation using a matrix would be to take the $3 \times 3$ matrix with entries $1$ corresponding to $(i,j)$ in the relation and $0$ otherwise.

$$ M = \pmatrix{1 & 1 & 1\cr 0 & 1 & 0\cr 1 & 1 & 1\cr}$$

Transitivity corresponds to the fact that $M^2 \ge M$.