Prove: $o(ab)=o(ba)$
34973
Is it true that the order of $ab$ is always equal to the order of $ba$?
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
110502
$AB=BA$ with same eigenvector matrix
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
6096
If $A+B=AB$ then $AB=BA$
152817
Proving $\sup B=\inf A$
66709
Are the matrix products $AB$ and $BA$ similar?
37061
The order of $ab$ when $a,b$ commute
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
106986
Eigenvalues of $AB$ and $BA$
83273
Show that $o(gHg^{-1})=o(H)$
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
78298
On the nilpotence of the matrix $AB-BA$
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
133699
Proving that there is a bijection between $A$ and $B$.
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.