Question
Determine whether the following operations define a binary operation on the given set or not: $\ '\times _6\ '$ on $S = {1, 2, 3, 4, 5}$ defined by, $a \times _6 b =$ Remainder when $ab$ is divided by $6.$
| $\times _6$ | $1$ | $2$ | $3$ | $4$ | $5$ |
| $1$ | $1$ | $2$ | $3$ | $4$ | $5$ |
| $2$ | $2$ | $4$ | $0$ | $2$ | $4$ |
| $3$ | $3$ | $0$ | $3$ | $0$ | $3$ |
| $4$ | $4$ | $2$ | $0$ | $4$ | $2$ |
| $5$ | $5$ | $4$ | $3$ | $2$ | $1$ |
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