Prove that each of the following subsets H of M2(R) is a subgroup of the group G ofall invertible matrices in M2(R) under multiplication.-{{: ]}{:1a-bа. Нb. Нa + bbа

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Answered: Prove that each of the following…

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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Let GL(2,11) be the group of all invertible 2 × 2 matrices with entries in Z₁1, with group operation given my matrix multiplication. Consider the following two matrices in this group (where an entry listed as k is shorthand for [k]11): 3 3 10 4- (1₂0). B- (B) A = B= 8 8 (ii) Consider the subset of GL(2,11) given by G= {Am B : m, n = Z}. Show that G is a subgroup of GL(2, 11).
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Prove that each of the following subsets H of M2(R) is a subgroup of the group G of all invertible matrices in M2(R) under multiplication. {: {: :] 1 a a -b а. Н - b. H = a + b a