Question

Prove that: If A or B is nonsingular, then AB is similar to BA

Matrix transformations
ANSWERED
asked 2020-11-08
Prove that: If A or B is nonsingular, then AB is similar to BA

Answers (1)

2020-11-09

We know two matrix M and N are said to be similar if thee exist an invertible matrix P such that \(\displaystyle{P}^{{-{{1}}}}{M}{P}={N}\)
Suppose that A is not singular. Therefore \(\displaystyle{A}^{{-{{1}}}}\) exist. Now \(AB=AB(AA^{-1}) =A(BA)A^{-1}\)
This shows that AB and BA are similar.

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...