Doubt regarding the proof of row rank = column rank
121157
Proof verification: column rank = row rank
6746
What is the Relationship between the Rank and the Number of Eigenvalues?
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
37162
Prove that matrices have equal rank.
152869
Rank of circulant matrix with $k$ ones per row
72578
Determinant value of a square matrix whose each entry is the g.c.d. of row and column position
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
114524
Proof Verification: the orthogonal complement of the column space is the left nullspace
55874
Row vector vs. Column vector
59944
How can I find the rank and spark relation here?
97487
How to prove whether a matrix has rank $1$
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?