Q)
Define a binary operation $\ast$ on the set {0, 1, 2, 3, 4, 5} as \[a*b=\left \{ \begin{array} {1 1} a+b, & \quad \text{ if a+b<6} \\ a+b-6, & \quad { if a+b \geq 6} \end{array} \right.\] show that the zero is the identity for this operation and each element $a \neq 0$ of the set is invertible with $6-a$ being the inverse of $a$.
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