Find the inverse of 5 under multiplication modulo 11 on Z11

A composition table consists of elements which are a result of an operation on the set elements.


Here we have the operation, a x11 b = remainder of ab divided by 11 where a, b S



Example, 4 x11 9 = Remainder of (4 x 9) divided by 11



For bS to be an inverse of aS, a x7b = e, where e is the identity element.


We know for multiplication operation we have the identity element as 1.


So e = 1.


For a = 5,


5 x11 (inverse of 3) = 1



From the table above, 5 x11 9 = 1.


Hence, i = 9.


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