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@zareen said in MTH633 Assignment 1 Solution and Discussion: Write down the elements of group under composition Test 0: Is the operation associative? If not, then you’re done. 𝑇(𝑆) is not a group. If the operation is associative, then proceed to… Test 1: Does the set 𝑇(𝑆) contains an identity? If you have a candidate function in 𝑇(𝑆), then what equations must it satisfy? Does it? If not, then 𝑇(𝑆) is not a group. If you do have an identity, then proceed to… Test 2: Does every element of 𝑇(𝑆) have an inverse? Given an arbitrary function in 𝑓∈𝑇(𝑆), can you write down its inverse 𝑓−1∈𝑇(𝑆)? What equation must 𝑓 and 𝑓−1 satisfy? (Hint: you need the identity function.) If any function fails to have an inverse, then 𝑇(𝑆) is not a group. If every function does have an inverse, then… Congratulations! Your set 𝑇(𝑆) is a group. Reff