For which ${n\in{\Bbb Z}}$ does there exist a matrix $P\in{\Bbb C}^{4\times 4}$ such that $P^n=M$?
122622
Does there exist a matrix $P$ such that $P^n=M$ for a special matrix $M$?
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
95227
Is the set of all $n\times n$ matrices, such that for a fixed matrix B  AB=BA, a subspace of the vector space of all $n\times n$ matrices?
120744
How many $n\times m$ binary matrices are there, up to row and column permutations?
141173
Are there matrices such that $AB=I$ and $BA \neq I$
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
137186
Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).
42883
Cross product in $\mathbb R^n$
85297
find a $3 \times 3$ matrix $A$ such that $A \neq I_3$ and $A^{197}=I_3$.
111366
Does there exist a symmetric matrix $A$ such that $2^{\sqrt{n}}\le |\operatorname{Tr}(A^n)|\le2020 \ \cdot 2^{\sqrt{n}}$ for all $n$
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
52951
Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
78298
On the nilpotence of the matrix $AB-BA$
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
120642
Let $g : \Bbb N \times \Bbb N \to\Bbb N \times \Bbb N$ defined as $g(m,n) = (m + n,m - n)$