Why If B is an invertible matrix, then rank(A) = rank(BA)?
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
110502
$AB=BA$ with same eigenvector matrix
87387
Linear equations given by $Ax = b$ have a solution if and only if $\operatorname{rank}(A|b) = \operatorname{rank}(A)$
111769
Why is inverse of orthogonal matrix is its transpose?
105921
Why do we have $ab=ba$?
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?
147014
Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
34043
A rank-one matrix is the product of two vectors
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 $\det(A)$?
134402
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
43000
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
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
125889
Determinant of rank-one perturbations of (invertible) matrices
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
158695
Prove that if $AB$ is invertible then $B$ is invertible.
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.