Let (G, o) be any group and let ϕ be the mapping: ϕ: G -> G

x -> x^-1

Prove that ϕ is 1to1, onto and that ϕ is an isomorphism if and only if G is abelian.

Abank manager wants to encourage new customers to open accounts with principals of at least $2 comma 500. he decides to make a poster advertising a simple interest rate of 3%. what must the principal be if the bank manager also wants to advertise that one can earn $10 the first month? can the poster correctly say, "open an account of $2 comma 500 and earn at least $10 interest in 1 month! "?