For G = <a: a^100 = e>, find the following

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SUMMARY

The discussion centers on finding the inverse of an element in a group defined by the equation G = a^100 = e. The participant initially calculated a^-5 as a^95 based on their understanding of inverses, but later corrected this to a^-5 = a^20. This highlights the importance of accurately applying the properties of group theory, specifically the relationship between elements and their inverses.

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CoachBryan
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It's asking me to find a^-5
From what I understood about inverses is that it's the element before you hit the identity would be the inverse. So a^5 = (a^5, a^10, a^15,..., a^90, a^95, a^100 = e), then a^-5 = a^95.

The correct answer is actually a^20.

Can anyone help me out with understanding inverses? Thanks!
 
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Nevermind, it was a typo. The answer was a^-5 = a^95
 

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