finding inverse to tell whether or not it is a group!

[Goistein]

I am trying to find inverse to determine whether a not an operational system! I'm really needing some help here!

key

Sq=Square
Tr=Triangle
Ci=Circle
St=Star

X Sq Tr Ci St
|---------------------
Sq| St Ci Tr Sq
Tr |Ci St Sq Tr
Ci |Tr Sq St Ci
St |Sq Tr Ci St

 

[stapel]

"Groups" are usually covered in post-calculus (graduate-level college) abstract-algebra courses. You have posted this to the pre-algebra category, so you must be doing something other than the usual meaning of "groups", "operations", and "inverses".

Please reply with a corrected posting of the text of the exercise, the complete instructions, and clear definitions of what you mean by the terms in play. Also, please clarify what is being done with the various listed shapes, what "X" means, and how you are "operating" on these shapes.

Thank you.

Eliz.

 

[daon]

Your identity will be Star since it leaves all elements of the group alone when acting on the right or left. That is Star * Triangle = Triangle * Star = Triangle, so e=Star.

To find inverses, note which element you need to multiply by to get your identity.
For example, the Inverse of Triange is Triangle, since Triangle*Triangle=Star. This group seems to have the property that all elements are their own inverses.

Daon