- #1
patelnjigar
- 24
- 0
Show that whenever ab = ba, you have ba^(-1) = a^(-1)b.
I don't know how to slove problem.
pls help me..
I don't know how to slove problem.
pls help me..
patelnjigar said:you mean that I have to make left and right..
make left:
ba^(-1) = a^(-1)b => aba^(-1) = aa^(-1)b
make right:
ba^(-1) = a^(-1)b => ba^(-1)a = a^(-1)ba
then what??
You started off correctly but made a typo (bolded) in the second step. Else you would have got the correct answer.patelnjigar said:ab=ba
a^(-1).ab.a^(-1) = a^(-1).ba.a^(-1)
(a^(-1).a) b^(-1) = a^(-1).b(a.a^(-1))
e.b^(-1) = a^(-1).b.e
b^(-1) = a^(-1).b
is that right?? I hope that I made it...
A Fintie Group is a mathematical concept that refers to a set of elements with a defined operation that satisfies certain properties, such as closure, associativity, identity, and invertibility.
A subgroup is a subset of a Fintie Group that also satisfies the properties of a Fintie Group. In other words, it is a smaller group within a larger group that shares the same operation and properties.
Fintie Groups and Subgroups are related in that Subgroups are subsets of Fintie Groups, and therefore share the same operation and properties. Additionally, Subgroups can be used to study and understand the properties and behavior of the larger Fintie Group.
Studying Fintie Groups and Subgroups is significant in mathematics because they have many real-world applications, such as in cryptography, coding theory, and computer science. They also provide a powerful tool for understanding and solving complex mathematical problems.
Fintie Groups and Subgroups are used in practical applications, such as in cryptography to encrypt and decrypt data, in coding theory to detect and correct errors in data transmission, and in computer science to design efficient algorithms and data structures.