Show that $\operatorname{rank}(A)=\operatorname{rank}(B)$
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
156877
Rank-one perturbation proof
61066
Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
125030
Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
22758
If $\operatorname{ran} F \subseteq \operatorname{dom} G$, then $\operatorname{dom}(G \circ F) = \operatorname{dom} F$.
77192
How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
71040
If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
76200
Is the rank of $AB$ always equal to the rank of $BA$?
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}