Will AB = BA always be true when A and B are nxn diagonal matrices? Explain why/why notWill AB = BA always be true when working with any matrices A and B? Explain why/why notGiven we know that a matrix B is the inverse of a matrix A when AB = BA = I the inverse of an nxn diagonal matrix A will sometimes exist. State what the the inverse matrix B is and when it exists (hint: what do we need to know about the diagonal entries of matrix A?).

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Answered: Will AB = BA always be true when A 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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Will AB = BA always be true when A and B are nxn diagonal matrices? Explain why/why not
Will AB = BA always be true when working with any matrices A and B? Explain why/why not
Given we know that a matrix B is the inverse of a matrix A when AB = BA = I the inverse of an nxn diagonal matrix A will sometimes exist. State what the the inverse matrix B is and when it exists (hint: what do we need to know about the diagonal entries of matrix A?).

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