Show that if $AB = BA$, then $\exp(A) \exp(B) = \exp(B) \exp(A)$
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
102742
order $a$ = 5, $a^3b = ba^3$. show that that $ab = ba$.
84422
$AB=BA$, $AC=CA$ we need to show $BC=CB$
140290
Solving $AB - BA = C$
76200
Is the rank of $AB$ always equal to the rank of $BA$?
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
158695
Prove that if $AB$ is invertible then $B$ is invertible.