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Define a binary operation $^*$ on the set A = {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 zero is an identity element for this operation and each element a of the set is invertiable with 6-a being the inverse of a.

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