Can we prove $BA=E$ from $AB=E$?
3301
If $AB = I$ then $BA = I$
58113
Av = Bv for all v implies A = B?
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
15416
A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.
55062
$2\times 2$ matrix $C=AB-BA$
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
76200
Is the rank of $AB$ always equal to the rank of $BA$?
78298
On the nilpotence of the matrix $AB-BA$
129007
Relation between AB and BA
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
105921
Why do we have $ab=ba$?
141173
Are there matrices such that $AB=I$ and $BA \neq I$
23946
Prove the definitions of $e$ to be equivalent
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.