If A is a $m\times n$ matrix, and $\text{rank}(A)=1$, then $A^2 =\lambda A$
130799
Matrix of rank 1; show that $A^2=cA$ for some scalar $c$.
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
9220
If $\lambda$ is an eigenvalue of $A^2$, then either $\sqrt{\lambda}$ or $-\sqrt{\lambda}$ is an eigenvalue of $A$
55031
Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
147014
Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
155451
Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$
34043
A rank-one matrix is the product of two vectors
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
152869
Rank of circulant matrix with $k$ ones per row
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
30866
Relation between rank and number of distinct eigenvalues of a matrix
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
128453
If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
80022
Eigenvector of A by $A^2$