Linear algebra, construction of counter example for two rectangular matrices such that $AB=I$ but $BA\neq I$
141173
Are there matrices such that $AB=I$ and $BA \neq I$
75104
Existence of some type matrix
78298
On the nilpotence of the matrix $AB-BA$
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
13026
Prove that if AB=I_m, then rk(A)=rk(B).
3301
If $AB = I$ then $BA = I$
130498
Linear algebra proof regarding matrices
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.
51406
Determinant of a block matrix times the determinant of the inverse of a block
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
123808
How would I solve the following problem involving elementary matrices?
55062
$2\times 2$ matrix $C=AB-BA$
38550
2x2 matrices with sum of diagonal entries equal zero
108850
Complex matrix that commutes with another complex matrix.
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
70606
Show that the LU decomposition of matrices of the form $\left[\begin{smallmatrix}0& x\\0 & y\end{smallmatrix}\right]$ is not unique
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?