6.2.30 Binary relations

Condition: For relations \( \alpha, \beta, \gamma \) defined on a finite set \( A=\{1,2,3,4,5,6\} \), find \[ \beta \cdot \gamma ; \gamma^{-1} \cdot \beta \cdot \alpha, \text { if } \alpha=\left(\begin{array}{llll} 3 & 4 & 2 & 1 \\ 4 & 1 & 6 & 3 \end{array}\right) \text {, } \] \[ \beta=\left(\begin{array}{lll} 6 & 1 & 4 \\ 2 & 3 & 3 \end{array}\right), \quad \gamma=\left(\begin{array}{lll} 6 & 1 & 4 \\ 2 & 3 & 3 \end{array}\right) \]