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?).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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  1. Will AB = BA always be true when A and B are nxn diagonal matrices? Explain why/why not
  2. Will AB = BA always be true when working with any matrices A and B? Explain why/why not
  3. 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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