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 PSKAB=AB(AA^-1) =A(BA)A^-1ZSK

This shows that AB and BA are similar.

Suppose that A is not singular. Therefore \(\displaystyle{A}^{{-{{1}}}}\) exist. Now PSKAB=AB(AA^-1) =A(BA)A^-1ZSK

This shows that AB and BA are similar.