Proving that $\operatorname{rank}(AB)$ is smaller or equal to $\operatorname{rank}(B)$
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
81618
Prove $||a|-|b| | \leq |a-b|$
134402
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
97487
How to prove whether a matrix has rank $1$
76200
Is the rank of $AB$ always equal to the rank of $BA$?
43000
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
78575
If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
156877
Rank-one perturbation proof
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
50266
In the following figure prove that: $AK||BC$
37924
Equivalence of norms proof
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$