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A binary operation * on the set {0,1,2,3...

A binary operation `*` on the set {0,1,2,3,4,5} is defined as
` a*b= {{:(a+b, "if" a+b lt 6),(a+b-6, "if" a +b gt=6):}`
Find the composition table for `*` Also, show that zero is the identity for this operation and each non-zero element a of the set is invertible with 6-a, being the inverse of a.

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