There do not exist $m\times n$ and $n\times m$ rectangular matrices $A$ and $B$ . t. $AB=I_m$ (The $m\times m$ Identity matrix)
56312
Why can this product of rectangular matrices not be the identity matrix?
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
3601
A problem about Vandemonde matrix
58339
The diagonalizable matrices are not dense in the square real matrices
141105
Show that there exists a $3 × 3$ invertible matrix $M$ with entries in $\mathbb{Z}/2\mathbb{Z}$ such that $M^7 = I_3$.
34536
Columns of matrix $A_{m \times n}$ span $\mathbb{R}^{m}$
139988
Counter example for a result of intersection of subspaces
52882
find nonsingular matrices $B$ and $C$ that satisfy $BC+ CB= 0$
75104
Existence of some type matrix
137081
Is the set of real matrices diagonalizable in $\mathcal M_n(C)$ dense in the set of all companion matrices?
52564
$m\times n$ matrix with an even number of 1s in each row and column
123726
$2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
58021
Finding matrix $B$ is not zero matrix where $AB= 0$
140252
Matrices - Conditions for $AB+BA=0$
27984
Square matrices satisfying certain relations must have dimension divisible by $3$
142642
$A=\begin{pmatrix}0&0&1\\ 0&1&0\\ 1&0&0\end{pmatrix}$, $X^2=A$ has no solutions