For each $n \in \mathbb{N}$, specify matrices $A, B \in \mathbb{R}^{n \times n}$ for which $A B \neq B A$ is true.
120937
Matrices that commute with all matrices
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
43326
Can every group be represented by a group of matrices?
52040
"Inverse" of an $n\times k$ matrix.
141858
$\forall \vec{b} \in \mathbb{R}^n, B \vec{x} = \vec{b}$ is consistent is equivalent to....
18145
Diagonalizable matrices with complex values are dense in set of $n\times n$ complex matrices.
75211
Theorem about positive matrices
31326
Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
48658
Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
22410
Find a symmetric matrix $B$ such that for every $3\times 1$ matrix $\text{x}$
55272
Prove that all nxn nilpotent matrices of order n are similar.
42883
Cross product in $\mathbb R^n$
12955
Classification of $n\times n$ real matrices up to congruence
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
120642
Let $g : \Bbb N \times \Bbb N \to\Bbb N \times \Bbb N$ defined as $g(m,n) = (m + n,m - n)$
87136
All matrices which commute with all $2\times 2$ matrices