rank(AB) = rank(A) if B is invertible
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
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?
131480
Proof that composition of invertible linear transformations is invertible (without determinants)
119435
Rank of the difference of matrices
97487
How to prove whether a matrix has rank $1$
3301
If $AB = I$ then $BA = I$
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
106398
If $A$ is invertible show that $\det(A) \neq 0$
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
158695
Prove that if $AB$ is invertible then $B$ is invertible.
97040
Question about an application of the Rank-Nullity theorem
121221
Rank-Nullity Theorem
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
27821
A problem on rank of $A$ and $\operatorname{adj}(A)$
42809
How can we show that $(I-A)$ is invertible?