Rank of matrix whose coefficients are $a_{i,j}=\gcd(i,j)$
72578
Determinant value of a square matrix whose each entry is the g.c.d. of row and column position
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
123151
Find the rank of matrix.
10483
Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$
41436
rank of complex conjugate transpose matrix property proof
134402
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
82925
Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?
155451
Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
137148
If $A=\left( \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{array} \right)$, find the rank of $A+A^2+A^3$
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
125889
Determinant of rank-one perturbations of (invertible) matrices
84279
The average determinant of all integer matrices with coefficients $0,1,2$
4952
Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
44898
Help with commutative property of matrices problem