If two invertible matrices A and B commute, so their inverse must commute as well or not ?
1 Answer
$\begingroup$
$\endgroup$
10
This follows from \begin{equation} A^{-1}B^{-1} = (BA)^{-1} = (AB)^{-1} = B^{-1}A^{-1}. \end{equation}
-
-
-
$\begingroup$ Is the equation (A+B)^2 =A^2+2AB+B^2 holds for all n*n matrices A and B ? $\endgroup$– RamyApr 12, 2015 at 10:14
-
$\begingroup$ @Ramy: Nope... you have $(A+B)^2 = A^2 + AB + BA + B^2$, and in general $AB \neq BA$. $\endgroup$– A.P.Apr 12, 2015 at 10:22
-
$\begingroup$ @A.P. : Could you tell me why ? or it's proof ? $\endgroup$– RamyApr 15, 2015 at 19:00