Define a binary operation ∗ on the set {0,1,2,3,4,5}as a∗b ={a+b, – InterviewSolution

1.	Define a binary operation ∗ on the set {0,1,2,3,4,5}as a∗b ={a+b, if a+b<6a+b−6,if a+b≥6 Show that zero is the identity for this operation and each element a≠0 of the set is invertible with (6-a) being the inverse of a.
Answer» Define a binary operation $$ on the set {0,1,2,3,4,5}as $a b$ $= {\begin{matrix} a + b, i f a + b < 6 a + b - 6, i f a + b \geq 6 \end{matrix}$ Show that 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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