Proving an $m\times n$ matrix has left and right inverse
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
137920
Proving an equation with invertible matrices
112353
Prove that all 2x2 orthogonal matrices can be expressed as Rotation or Reflection
145447
bilinear form - proof
145768
The inverse of a matrix in which the sum of each row is $1$
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
48009
Left inverse implies right inverse in a finite ring
6324
Deriving the inverse of a 2x2 matrix
33355
Proving that matrix in equation is invertible
23372
Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set
42467
Inverse of an invertible triangular matrix (either upper or lower) is triangular of the same kind
102529
Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
58491
Proving the inverse of a matrix as a polynomial of matrices
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$