The non-existence of a matrix $A\in M_3(\mathbb{R})$ such that $A^2-A+I=0$.
137209
Finding the Matrix of a Linear Operator Satisfying a Polynomial
37537
Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
38635
How to prove that the matrix $A^k$ approaches $0$ as $k$ approaches infinity
23301
There does not exist any integer $m$ such that $3n^2+3n+7=m^3$
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
104653
$A$ and $B$ are $3\times 3$ real matrices such that $\operatorname{rank}(AB)=1$, then $\operatorname{rank}(BA$) can not be which of the following?
38550
2x2 matrices with sum of diagonal entries equal zero
75104
Existence of some type matrix
141105
Show that there exists a $3 × 3$ invertible matrix $M$ with entries in $\mathbb{Z}/2\mathbb{Z}$ such that $M^7 = I_3$.
127799
Eigenvalues of symmetric matrices are real without (!) complex numbers
56727
Odd-dimensional complex skew-symmetric matrix has eigenvalue $0$
7622
$AB-BA=I$ having no solutions
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
70157
Is every matrix $A$ such that $A^k=I$ diagonalizable?
86841
Find a matrix $B$ such that $B^3 = A$
129583
Find 3x3 real matrix A such that $A^2 \neq I$ and $A^4 = I$, where I is identity matrix.
51800
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$