If $A \in M(n,\mathbb R)$ , and rank of $A$ is $m$ , then what is the rank of the adjugate of $A$?
4205
Is adjoint of singular matrix singular? What would be its rank?
59396
Show that the rank of $A+B$ is no more than the sum of the ranks of $A$ and $B$
46128
Representation of Matrix with Rank 1
63036
Proving that $\dim(\mathrm{span}({I_n,A,A^2,...})) \leq n$
97487
How to prove whether a matrix has rank $1$
78575
If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$
55820
If $A$ is an $n \times n$ matrix and $ A^2 = 0$, then $\text{rank}(A)\le n/2$.
33451
Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
132366
Diagonalizability of $A \in M_{n}(\Bbb{R})$ (Upper traingular matrix) with all diagonal entries 1 and $A \neq I$?
137093
What is the codimension of matrices of rank $r$ as a manifold?
77192
How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
44383
Finding rank of a matrix depending on parameter a
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$