Matrices $A$ and $B$ so that $AB=I$ but $BA \ne I$
3301
If $AB = I$ then $BA = I$
13948
Matrix in a matrix
123555
Proving that if $ab=e$ then $ba=e$
78755
If matrix $A$ is unitary and $B^2=A$, is $B$ necessarily unitary?
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
59397
Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
147490
If matrix $AB=A$, does it mean B must be an identity matrix?
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
106322
Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
122622
Does there exist a matrix $P$ such that $P^n=M$ for a special matrix $M$?
15416
A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.
25357
Matrices $B$ that commute with every matrix commuting with $A$