Show that, for square matrices $A$ and $B$, $A+B=AB$ implies $AB=BA$.
74460
Matrices A+B=AB implies A commutes with B
25907
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
18528
Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
33560
Show that matrices $A$ and $B$ commute if and only if $\begin{vmatrix} b & a-c \\ e & d-f\end{vmatrix}=0.$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
3330
Square matrices, ABA = A?
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
133699
Proving that there is a bijection between $A$ and $B$.
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
63920
Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$?
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
9574
How to show that $\det(AB) =\det(A) \det(B)$?
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
158695
Prove that if $AB$ is invertible then $B$ is invertible.