16.Let R* be the multiplicative group of non zero real numbers and let S=R-{-1} bethe group under the operation defined byaab=a+b + ab.Define the mapping f: R*-S by f(r) = r - 1. Show that R* = S. 13.Let ne Z* and G=GL(R) the multiplicative group of all invertible nxn matrices overR. Show thatH = {A E G | det A = 1}is a subgroup of G.9

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Answered: 16. Let R* be the multiplicative group…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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16. Let R* be the multiplicative group of non zero real numbers and let S =R-{-1} be the group under the operation defined by aab=a+b+ ab. Define the mapping f: R* S by f(r) = r - 1. Show that R* = S.