If $A$ and $B$ are square matrix such that $AB=I$ then $BA=I$ too.
3301
If $AB = I$ then $BA = I$
85167
When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
36314
If $Ax = Bx$ for all $x \in C^{n}$, then $A = B$.
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
130498
Linear algebra proof regarding matrices
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
94037
Solving the matrix equation $AP=PB$, where $A$ and $B$ are similar
152693
If $C|a$ and $C|b$ then $C|(ax+by)$
147490
If matrix $AB=A$, does it mean B must be an identity matrix?
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
140252
Matrices - Conditions for $AB+BA=0$
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
33542
When is $A- B = B- A$?
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?