Please solve the problem as soon as possible Recall the following groups:Z4 = {0, 1, 2, 3} (operation: addition mod 4)Z = {1,5, 7, 11} (operation: multiplication mod 12)Z = {1,3, 5, 9, 11, 13} (operation: multiplication mod 14)%3D%3!%3D(operation: matrix multiplication)Find the order of each element of Z4, Z, ZiA, and GL(2, Z2).

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Answered: Recall the following groups: Z = {0, 1,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Recall the following groups: Z = {0, 1, 2, 3} (operation: addition mod 4) Z = {1,5, 7, 11} (operation: multiplication mod 12) Z = {1,3, 5 ,9, 11, 13} (operation: multiplication mod 14) %3D %3D %3D %3D (operation: matrix multiplication) Find the order of each element of Z, Z, Z, and GL(2, Z2).