How to prove $\operatorname{rank}{(AB)} = \operatorname{rank}{A}$?
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
147827
How to calculate $|\operatorname {SL}_2(\mathbb Z/N\mathbb Z)|$?
76200
Is the rank of $AB$ always equal to the rank of $BA$?
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
69606
How to prove rank(A+) is no more than rank(A)?
110381
Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
147659
Counterexample to "if $f:A\to A$ induces the identity $\hat f:\operatorname{Spec}(A)\to\operatorname{Spec}(A)$, then $f=\operatorname{id}_A$"
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
37061
The order of $ab$ when $a,b$ commute
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$