$AB-BA$ invertible and $A^2+B^2 = AB$ then $3$ divides $n$
27984
Square matrices satisfying certain relations must have dimension divisible by $3$
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
50534
Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
78298
On the nilpotence of the matrix $AB-BA$
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
3301
If $AB = I$ then $BA = I$
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
9302
Questions about Divisibility of $2^n$ by $3$
130825
How to factor intricate polynomial $ ab^3 - a^3b + a^3c -ac^3 +bc^3 - b^3c $
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
127293
Prove that $(a-b) \mid (a^n-b^n)$
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
158695
Prove that if $AB$ is invertible then $B$ is invertible.