Does there exist a $2×2$ matrix such that $A^2 \neq 0$ but $A^3=0$?
41411
How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$
38635
How to prove that the matrix $A^k$ approaches $0$ as $k$ approaches infinity
15730
Determine the minimum of $a^2 + b^2$ if $a,b\in\mathbb{R}$ are such that $x^4 + ax^3 + bx^2 + ax + 1 = 0$ has at least one real solution
11857
$A$ be a complex $3\times 3$ matrix such that $A^3=-I$
139685
If $A^2$ and $B^2$ are similar matrices, do $A$ and $B$ have to be similar?
116539
Eigenvalues of matrix satisfying $A^2 = A$
109736
For a 2x2 matrix A satisfying $A^k=I$, compute $e^A$
47012
When a 0-1-matrix with exactly two 1’s on each column and on each row is non-degenerated? [1]
3330
Square matrices, ABA = A?
110271
Given a matrix with non-negative real entries, can you algebraically prove that it has a non-negative eigenvalue?
121062
Given a matrix, is there always another matrix which commutes with it?
38550
2x2 matrices with sum of diagonal entries equal zero
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
40222
Matrices that are not diagonal or triangular, whose eigenvalues are the diagonal elements
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
11620
Is it true that any matrix in $M_2(\mathbb R)$ is the sum of two squares?