$A,B \in M(n,\mathbb C)$ with $AB=BA$ , then does there exist $P \in M(n,\mathbb C)$ and $f(X) , g(X) \in \mathbb C[X]$ such that $A=f(P), B=g(P)$?
57731
Can commuting matrices $X,Y$ always be written as polynomials of some matrix $A$?
90649
Consider $f(x)=mx$ and $g(x) =bx$ in which $m>0$ and $b>0$. Does there exist any homeomorphism $h$ such that $h \circ f$ = $g \circ h$
34973
Is it true that the order of $ab$ is always equal to the order of $ba$?
67717
$A \oplus B = A \oplus C$ imply $B = C$?
6825
If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
89190
Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
45760
if G is generated by {a,b} and ab=ba, then prove G is Abelian
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
66709
Are the matrix products $AB$ and $BA$ similar?
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
130297
$A$ be a subset of $[0,1]$ with non-empty interior ; then is it true that $\mathbb Q+A=\mathbb R$?
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$