Matrix commutation with an inverse
= Matrix commutation with an inverse
{title2=$AB=BA\implies AB^{-1}=B^{-1}A$}
If two square <matrices> satisfy $AB=BA$ and $B$ is invertible, multiplication on the left and right by $B^{-1}$ gives $B^{-1}A=AB^{-1}$. Consequently a polynomial in a <matrix> commutes with the <matrix inverse> of any invertible polynomial in the same <matrix>.