How to show that if $A, B$, and $A + B$ are invertible matrices with the same size, then $A(A^{ −1} + B^{ −1} )B(A + B)^ {−1} = I$
75215
Properties of invertible matrices
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
58491
Proving the inverse of a matrix as a polynomial of matrices
74460
Matrices A+B=AB implies A commutes with B
75066
If the product of two square matrices is invertible, then both matrices are invertible
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
6398
Can the product of an $4\times 3$ matrix and a $3\times 4$ matrix be invertible?
64747
If $A^m=I$ then A is Diagonalizable
126018
Show that $ e^{A+B}=e^A e^B$
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
33560
Show that matrices $A$ and $B$ commute if and only if $\begin{vmatrix} b & a-c \\ e & d-f\end{vmatrix}=0.$
13026
Prove that if AB=I_m, then rk(A)=rk(B).
63920
Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$?
37162
Prove that matrices have equal rank.
35080
If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$