Showing that if $AB=BA$ then $A$ and $B$ are simultaneously diagonalizable
36613
Prove that simultaneously diagonalizable matrices commute
13026
Prove that if AB=I_m, then rk(A)=rk(B).
55062
$2\times 2$ matrix $C=AB-BA$
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
75066
If the product of two square matrices is invertible, then both matrices are invertible
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
135316
A basic question on diagonalizability of a matrix
141173
Are there matrices such that $AB=I$ and $BA \neq I$
3682
If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable
106986
Eigenvalues of $AB$ and $BA$
59397
Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
110502
$AB=BA$ with same eigenvector matrix
35080
If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$
18800
If A and B are symmetric is AB=BA true?
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique