Show that AB - BA = I is impossible for n x n matrices of real or complex numbers.
7622
$AB-BA=I$ having no solutions
67208
Can we say that there exist an integer $n$ such $A+nB$ invertible?
113474
An $n \times n$ matrix $M$ of integers has the property that $M_{ab} = M_{xy}$ iff $a+b=x+y$. How many distinct elements are there in $M$?
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
127799
Eigenvalues of symmetric matrices are real without (!) complex numbers
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
140290
Solving $AB - BA = C$
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
83116
Uncountability of basis of $\mathbb R^{\mathbb N}$
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
54294
Can the product $AB$ be computed using only $+, -,$ and reciprocal operators?
137081
Is the set of real matrices diagonalizable in $\mathcal M_n(C)$ dense in the set of all companion matrices?
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
146243
Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
106986
Eigenvalues of $AB$ and $BA$