Linear Algebra - Matrix Multiplication

[jofree87]

| 1 1 1 | = matrix A
| 1 2 3 |
| 1 4 5 |

How do I find a 3x3 matrix B, excluding the identity or zero matrix, such that AB = BA?

 

[Roni1985]

I think if you create and multiply by a diagonal matrix, it would work.
I know for sure that if A and B are diagonal matrices, AB=BA

 

[mmmboh]

You could make a matrix of entries a b c d e f g h i and let that be matrix B,and you can then multiply AB and BA, and equate each entry or make a system of equations out of it and find what value each letter has in terms of the other letters. There may be an easier way I'm tired.

 

[Mark44]

| 1 1 1 | = matrix A
| 1 2 3 |
| 1 4 5 |

How do I find a 3x3 matrix B, excluding the identity or zero matrix, such that AB = BA?

The inverse of A, A^-1, is a matrix for which AA^-1 = A^-1A. Do you know how to find the inverse of a given matrix?