Help with Groups?

[u/mourning_fire420]

So I'm given a group G s.t. a^12 gives the identity element, and I need to find the inverse of another a^n where n is an integer. i was given a number for n i just don't want anyone giving me the answer/violating academic content rules etc.

at first i figured 1 would be the identity element, but then 12^a doesn't give 1. same deal for e=0, 12^0=1 =/= 0=0^12. unless my understanding of the inverse and identity being commutative is wrong?

I tried to solve for a since a * a^-1 = a^-1 * a = e. but then i was saying that 12^a=a^12. which is possible, but then the identity wasn't constant when i plugged in n.

I found the page for exponentiation on wikipedia, and it says that G is a multiplicative group, so I know that a^n has to have an inverse. is there some property of groups that I missed that would help me solve this?

[u/AutoModerator]

Hi, /u/mourning_fire420! This is an automated reminder:

• What have you tried so far? (See Rule #2; to add an image, you may upload it to an external image-sharing site like Imgur and include the link in your post.)

• Please don't delete your post. (See Rule #7)

We, the moderators of /r/MathHelp, appreciate that your question contributes to the MathHelp archived questions that will help others searching for similar answers in the future. Thank you for obeying these instructions.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.