Let B be an invertible matrix nx n and M₁ (R) be the space of allnxn metrices. Prove that the map f: M₂ (R) → M₂ (R) defined by f(A) = AB is a bijectiveendomorphism.

Given: B is an invertible matrix . To Prove : A map f: MnR→MnR define by fA=AB is a bijective…

Answered: Let B be an invertible matrix nx n and…

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 B be an invertible matrix nx n and M. (R) be the space of all nx n metrices. Prove that the map f: M₂ (R) → M₂ (R) defined by f(A) = AB is a bijective endomorphism.