For square matrices $ (AB)^k=I_n$ for some $k$ implies $(BA)^k=I_n$
34973
Is it true that the order of $ab$ is always equal to the order of $ba$?
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
6091
Similarity of products $AB$ and $BA$ of square matrices
3330
Square matrices, ABA = A?
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
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.
59397
Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
72507
Does $ab=1$ imply $ba=1$ in a ring?
116136
Proof that the inverse of a square matrix is unique
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
105180
When does $(ab)^n = a^n b^n$ imply a group is abelian?
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
123726
$2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
64747
If $A^m=I$ then A is Diagonalizable
15626
Relations of a~b iff b = ak^2