(2) Let X be the set {1,2,3,4,5,6,7}, and define an operation on X to be multiplication modulo 8. (Notice we've left out

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2 Let X Be The Set 1 2 3 4 5 6 7 And Define An Operation On X To Be Multiplication Modulo 8 Notice We Ve Left Out 1 (29.47 KiB) Viewed 78 times

(2) Let X be the set {1,2,3,4,5,6,7}, and define an operation on X to be multiplication modulo 8. (Notice we've left out zero.) Make a Cayley table for X with this operation. Is it closed (i.e. a binary operation)? Is X associative? Is there an identity element? Which elements have an inverse? Is X a group? (3) Do the same as the previous problem, but with the set {1, 2, 3, 4, 5,6}, and multiplication mod 7.